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differential equation (PDE)</title> <meta name="description" content="Search results for: partial differential equation (PDE)"> <meta name="keywords" content="partial differential equation (PDE)"> <meta name="viewport" content="width=device-width, initial-scale=1, minimum-scale=1, maximum-scale=1, user-scalable=no"> <meta charset="utf-8"> <link href="https://cdn.waset.org/favicon.ico" type="image/x-icon" rel="shortcut icon"> <link href="https://cdn.waset.org/static/plugins/bootstrap-4.2.1/css/bootstrap.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/plugins/fontawesome/css/all.min.css" rel="stylesheet"> <link href="https://cdn.waset.org/static/css/site.css?v=150220211555" rel="stylesheet"> </head> <body> <header> <div class="container"> <nav class="navbar navbar-expand-lg navbar-light"> <a class="navbar-brand" href="https://waset.org"> <img src="https://cdn.waset.org/static/images/wasetc.png" alt="Open Science Research Excellence" title="Open Science Research 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method="get" action="https://publications.waset.org/abstracts/search"> <div id="custom-search-input"> <div class="input-group"> <i class="fas fa-search"></i> <input type="text" class="search-query" name="q" placeholder="Author, Title, Abstract, Keywords" value="partial differential equation (PDE)"> <input type="submit" class="btn_search" value="Search"> </div> </div> </form> </div> </div> <div class="row mt-3"> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Commenced</strong> in January 2007</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Frequency:</strong> Monthly</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Edition:</strong> International</div> </div> </div> <div class="col-sm-3"> <div class="card"> <div class="card-body"><strong>Paper Count:</strong> 4286</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: partial differential equation (PDE)</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4286</span> Study and Solving Partial Differential Equation of Danel Equation in the Vibration Shells </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hesamoddin%20Abdollahpour">Hesamoddin Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayeh%20Abdollahpour"> Roghayeh Abdollahpour</a>, <a href="https://publications.waset.org/abstracts/search?q=Elham%20Rahgozar"> Elham Rahgozar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper we deal with an analysis of the free vibrations of the governing partial differential equation that it is Danel equation in the shells. The problem considered represents the governing equation of the nonlinear, large amplitude free vibrations of the hinged shell. A new implementation of the new method is presented to obtain natural frequency and corresponding displacement on the shell. Our purpose is to enhance the ability to solve the mentioned complicated partial differential equation (PDE) with a simple and innovative approach. The results reveal that this new method to solve Danel equation is very effective and simple, and can be applied to other nonlinear partial differential equations. It is necessary to mention that there are some valuable advantages in this way of solving nonlinear differential equations and also most of the sets of partial differential equations can be answered in this manner which in the other methods they have not had acceptable solutions up to now. We can solve equation(s), and consequently, there is no need to utilize similarity solutions which make the solution procedure a time-consuming task. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=large%20amplitude" title="large amplitude">large amplitude</a>, <a href="https://publications.waset.org/abstracts/search?q=free%20vibrations" title=" free vibrations"> free vibrations</a>, <a href="https://publications.waset.org/abstracts/search?q=analytical%20solution" title=" analytical solution"> analytical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Danell%20Equation" title=" Danell Equation"> Danell Equation</a>, <a href="https://publications.waset.org/abstracts/search?q=diagram%20of%20phase%20plane" title=" diagram of phase plane "> diagram of phase plane </a> </p> <a href="https://publications.waset.org/abstracts/66849/study-and-solving-partial-differential-equation-of-danel-equation-in-the-vibration-shells" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/66849.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">320</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4285</span> Image Transform Based on Integral Equation-Wavelet Approach</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yuan%20Yan%20Tang">Yuan Yan Tang</a>, <a href="https://publications.waset.org/abstracts/search?q=Lina%20Yang"> Lina Yang</a>, <a href="https://publications.waset.org/abstracts/search?q=Hong%20Li"> Hong Li</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Harmonic model is a very important approximation for the image transform. The harmanic model converts an image into arbitrary shape; however, this mode cannot be described by any fixed functions in mathematics. In fact, it is represented by partial differential equation (PDE) with boundary conditions. Therefore, to develop an efficient method to solve such a PDE is extremely significant in the image transform. In this paper, a novel Integral Equation-Wavelet based method is presented, which consists of three steps: (1) The partial differential equation is converted into boundary integral equation and representation by an indirect method. (2) The boundary integral equation and representation are changed to plane integral equation and representation by boundary measure formula. (3) The plane integral equation and representation are then solved by a method we call wavelet collocation. Our approach has two main advantages, the shape of an image is arbitrary and the program code is independent of the boundary. The performance of our method is evaluated by numerical experiments. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=harmonic%20model" title="harmonic model">harmonic model</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation%20%28PDE%29" title=" partial differential equation (PDE)"> partial differential equation (PDE)</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equation" title=" integral equation"> integral equation</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20representation" title=" integral representation"> integral representation</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20measure%20formula" title=" boundary measure formula"> boundary measure formula</a>, <a href="https://publications.waset.org/abstracts/search?q=wavelet%20collocation" title=" wavelet collocation"> wavelet collocation</a> </p> <a href="https://publications.waset.org/abstracts/3920/image-transform-based-on-integral-equation-wavelet-approach" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3920.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">558</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4284</span> Application of Wavelet Based Approximation for the Solution of Partial Integro-Differential Equation Arising from Viscoelasticity</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Somveer%20Singh">Somveer Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Vineet%20Kumar%20Singh"> Vineet Kumar Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This work contributes a numerical method based on Legendre wavelet approximation for the treatment of partial integro-differential equation (PIDE). Operational matrices of Legendre wavelets reduce the solution of PIDE into the system of algebraic equations. Some useful results concerning the computational order of convergence and error estimates associated to the suggested scheme are presented. Illustrative examples are provided to show the effectiveness and accuracy of proposed numerical method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=legendre%20wavelets" title="legendre wavelets">legendre wavelets</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation" title=" partial integro-differential equation"> partial integro-differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=viscoelasticity" title=" viscoelasticity"> viscoelasticity</a> </p> <a href="https://publications.waset.org/abstracts/57515/application-of-wavelet-based-approximation-for-the-solution-of-partial-integro-differential-equation-arising-from-viscoelasticity" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/57515.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">448</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4283</span> Numerical Solutions of an Option Pricing Rainfall Derivatives Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Clarinda%20Vitorino%20Nhangumbe">Clarinda Vitorino Nhangumbe</a>, <a href="https://publications.waset.org/abstracts/search?q=Erc%C3%ADlia%20Sousa"> Ercília Sousa</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Weather derivatives are financial products used to cover non catastrophic weather events with a weather index as the underlying asset. The rainfall weather derivative pricing model is modeled based in the assumption that the rainfall dynamics follows Ornstein-Uhlenbeck process, and the partial differential equation approach is used to derive the convection-diffusion two dimensional time dependent partial differential equation, where the spatial variables are the rainfall index and rainfall depth. To compute the approximation solutions of the partial differential equation, the appropriate boundary conditions are suggested, and an explicit numerical method is proposed in order to deal efficiently with the different choices of the coefficients involved in the equation. Being an explicit numerical method, it will be conditionally stable, then the stability region of the numerical method and the order of convergence are discussed. The model is tested for real precipitation data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20differences%20method" title="finite differences method">finite differences method</a>, <a href="https://publications.waset.org/abstracts/search?q=ornstein-uhlenbeck%20process" title=" ornstein-uhlenbeck process"> ornstein-uhlenbeck process</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations%20approach" title=" partial differential equations approach"> partial differential equations approach</a>, <a href="https://publications.waset.org/abstracts/search?q=rainfall%20derivatives" title=" rainfall derivatives"> rainfall derivatives</a> </p> <a href="https://publications.waset.org/abstracts/169674/numerical-solutions-of-an-option-pricing-rainfall-derivatives-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/169674.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">106</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4282</span> Partial Differential Equation-Based Modeling of Brain Response to Stimuli</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Razieh%20Khalafi">Razieh Khalafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The brain is the information processing centre of the human body. Stimuli in the form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research, we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modelling of EEG signal in case external stimuli but it can be used for modelling of brain response in case of internal stimuli. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=brain" title="brain">brain</a>, <a href="https://publications.waset.org/abstracts/search?q=stimuli" title=" stimuli"> stimuli</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=response" title=" response"> response</a>, <a href="https://publications.waset.org/abstracts/search?q=EEG%20signal" title=" EEG signal"> EEG signal</a> </p> <a href="https://publications.waset.org/abstracts/29783/partial-differential-equation-based-modeling-of-brain-response-to-stimuli" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/29783.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">554</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4281</span> A Study of Non Linear Partial Differential Equation with Random Initial Condition</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayaz%20Ahmad">Ayaz Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this work, we present the effect of noise on the solution of a partial differential equation (PDE) in three different setting. We shall first consider random initial condition for two nonlinear dispersive PDE the non linear Schrodinger equation and the Kortteweg –de vries equation and analyse their effect on some special solution , the soliton solutions.The second case considered a linear partial differential equation , the wave equation with random initial conditions allow to substantially decrease the computational and data storage costs of an algorithm to solve the inverse problem based on the boundary measurements of the solution of this equation. Finally, the third example considered is that of the linear transport equation with a singular drift term, when we shall show that the addition of a multiplicative noise term forbids the blow up of solutions under a very weak hypothesis for which we have finite time blow up of a solution in the deterministic case. Here we consider the problem of wave propagation, which is modelled by a nonlinear dispersive equation with noisy initial condition .As observed noise can also be introduced directly in the equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=drift%20term" title="drift term">drift term</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20time%20blow%20up" title=" finite time blow up"> finite time blow up</a>, <a href="https://publications.waset.org/abstracts/search?q=inverse%20problem" title=" inverse problem"> inverse problem</a>, <a href="https://publications.waset.org/abstracts/search?q=soliton%20solution" title=" soliton solution"> soliton solution</a> </p> <a href="https://publications.waset.org/abstracts/77445/a-study-of-non-linear-partial-differential-equation-with-random-initial-condition" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/77445.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">215</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4280</span> Algorithms Utilizing Wavelet to Solve Various Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=K.%20P.%20Mredula">K. P. Mredula</a>, <a href="https://publications.waset.org/abstracts/search?q=D.%20C.%20Vakaskar"> D. C. Vakaskar </a> </p> <p class="card-text"><strong>Abstract:</strong></p> The article traces developments and evolution of various algorithms developed for solving partial differential equations using the significant combination of wavelet with few already explored solution procedures. The approach depicts a study over a decade of traces and remarks on the modifications in implementing multi-resolution of wavelet, finite difference approach, finite element method and finite volume in dealing with a variety of partial differential equations in the areas like plasma physics, astrophysics, shallow water models, modified Burger equations used in optical fibers, biology, fluid dynamics, chemical kinetics etc. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=multi-resolution" title="multi-resolution">multi-resolution</a>, <a href="https://publications.waset.org/abstracts/search?q=Haar%20Wavelet" title=" Haar Wavelet"> Haar Wavelet</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20methods" title=" numerical methods"> numerical methods</a> </p> <a href="https://publications.waset.org/abstracts/59280/algorithms-utilizing-wavelet-to-solve-various-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59280.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">299</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4279</span> Solving Stochastic Eigenvalue Problem of Wick Type</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Hassan%20Manouzi">Hassan Manouzi</a>, <a href="https://publications.waset.org/abstracts/search?q=Taous-Meriem%20Laleg-Kirati"> Taous-Meriem Laleg-Kirati</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we study mathematically the eigenvalue problem for stochastic elliptic partial differential equation of Wick type. Using the Wick-product and the Wiener-Ito chaos expansion, the stochastic eigenvalue problem is reformulated as a system of an eigenvalue problem for a deterministic partial differential equation and elliptic partial differential equations by using the Fredholm alternative. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. Once this approximation is performed, the statistics of the numerical solution can be easily evaluated. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=eigenvalue%20problem" title="eigenvalue problem">eigenvalue problem</a>, <a href="https://publications.waset.org/abstracts/search?q=Wick%20product" title=" Wick product"> Wick product</a>, <a href="https://publications.waset.org/abstracts/search?q=SPDEs" title=" SPDEs"> SPDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20element" title=" finite element"> finite element</a>, <a href="https://publications.waset.org/abstracts/search?q=Wiener-Ito%20chaos%20expansion" title=" Wiener-Ito chaos expansion"> Wiener-Ito chaos expansion</a> </p> <a href="https://publications.waset.org/abstracts/7652/solving-stochastic-eigenvalue-problem-of-wick-type" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/7652.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">359</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4278</span> On the Relation between λ-Symmetries and μ-Symmetries of Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teoman%20Ozer">Teoman Ozer</a>, <a href="https://publications.waset.org/abstracts/search?q=Ozlem%20Orhan"> Ozlem Orhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This study deals with symmetry group properties and conservation laws of partial differential equations. We give a geometrical interpretation of notion of μ-prolongations of vector fields and of the related concept of μ-symmetry for partial differential equations. We show that these are in providing symmetry reduction of partial differential equations and systems and invariant solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%CE%BB-symmetry" title="λ-symmetry">λ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=%CE%BC-symmetry" title=" μ-symmetry"> μ-symmetry</a>, <a href="https://publications.waset.org/abstracts/search?q=classification" title=" classification"> classification</a>, <a href="https://publications.waset.org/abstracts/search?q=invariant%20solution" title=" invariant solution"> invariant solution</a> </p> <a href="https://publications.waset.org/abstracts/59662/on-the-relation-between-l-symmetries-and-m-symmetries-of-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/59662.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">319</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4277</span> Large Amplitude Vibration of Sandwich Beam</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Youssef%20Abdelli">Youssef Abdelli</a>, <a href="https://publications.waset.org/abstracts/search?q=Rachid%20Nasri"> Rachid Nasri</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The large amplitude free vibration analysis of three-layered symmetric sandwich beams is carried out using two different approaches. The governing nonlinear partial differential equations of motion in free natural vibration are derived using Hamilton's principle. The formulation leads to two nonlinear partial differential equations that are coupled both in axial and binding deformations. In the first approach, the method of multiple scales is applied directly to the governing equation that is a nonlinear partial differential equation. In the second approach, we discretize the governing equation by using Galerkin's procedure and then apply the shooting method to the obtained ordinary differential equations. In order to check the validity of the solutions obtained by the two approaches, they are compared with the solutions obtained by two approaches; they are compared with the solutions obtained numerically by the finite difference method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=finite%20difference%20method" title="finite difference method">finite difference method</a>, <a href="https://publications.waset.org/abstracts/search?q=large%20amplitude%20vibration" title=" large amplitude vibration"> large amplitude vibration</a>, <a href="https://publications.waset.org/abstracts/search?q=multiple%20scales" title=" multiple scales"> multiple scales</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20vibration" title=" nonlinear vibration"> nonlinear vibration</a> </p> <a href="https://publications.waset.org/abstracts/35464/large-amplitude-vibration-of-sandwich-beam" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35464.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">463</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4276</span> The Non-Uniqueness of Partial Differential Equations Options Price Valuation Formula for Heston Stochastic Volatility Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20D.%20Ibrahim">H. D. Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=H.%20C.%20Chinwenyi"> H. C. Chinwenyi</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20Danjuma"> T. Danjuma</a> </p> <p class="card-text"><strong>Abstract:</strong></p> An option is defined as a financial contract that provides the holder the right but not the obligation to buy or sell a specified quantity of an underlying asset in the future at a fixed price (called a strike price) on or before the expiration date of the option. This paper examined two approaches for derivation of Partial Differential Equation (PDE) options price valuation formula for the Heston stochastic volatility model. We obtained various PDE option price valuation formulas using the riskless portfolio method and the application of Feynman-Kac theorem respectively. From the results obtained, we see that the two derived PDEs for Heston model are distinct and non-unique. This establishes the fact of incompleteness in the model for option price valuation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Black-Scholes%20partial%20differential%20equations" title="Black-Scholes partial differential equations">Black-Scholes partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Ito%20process" title=" Ito process"> Ito process</a>, <a href="https://publications.waset.org/abstracts/search?q=option%20price%20valuation" title=" option price valuation"> option price valuation</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a> </p> <a href="https://publications.waset.org/abstracts/131307/the-non-uniqueness-of-partial-differential-equations-options-price-valuation-formula-for-heston-stochastic-volatility-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131307.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">145</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4275</span> The Solution of Nonlinear Partial Differential Equation for The Phenomenon of Instability in Homogeneous Porous Media by Homotopy Analysis Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kajal%20K.%20Patel">Kajal K. Patel</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20N.%20Mehta"> M. N. Mehta</a>, <a href="https://publications.waset.org/abstracts/search?q=T.%20R.%20Singh"> T. R. Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> When water is injected in oil formatted area in secondary oil recovery process the instability occurs near common interface due to viscosity difference of injected water and native oil. The governing equation gives rise to the non-linear partial differential equation and its solution has been obtained by Homotopy analysis method with appropriate guess value of the solution together with some conditions and standard relations. The solution gives the average cross-sectional area occupied by the schematic fingers during the occurs of instability phenomenon. The numerical and graphical presentation has developed by using Maple software. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=capillary%20pressure" title="capillary pressure">capillary pressure</a>, <a href="https://publications.waset.org/abstracts/search?q=homotopy%20analysis%20method" title=" homotopy analysis method"> homotopy analysis method</a>, <a href="https://publications.waset.org/abstracts/search?q=instability%20phenomenon" title=" instability phenomenon"> instability phenomenon</a>, <a href="https://publications.waset.org/abstracts/search?q=viscosity" title=" viscosity "> viscosity </a> </p> <a href="https://publications.waset.org/abstracts/15845/the-solution-of-nonlinear-partial-differential-equation-for-the-phenomenon-of-instability-in-homogeneous-porous-media-by-homotopy-analysis-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/15845.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">496</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4274</span> Development of a Model Based on Wavelets and Matrices for the Treatment of Weakly Singular Partial Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Somveer%20Singh">Somveer Singh</a>, <a href="https://publications.waset.org/abstracts/search?q=Vineet%20Kumar%20Singh"> Vineet Kumar Singh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a new model based on viscoelasticity for the Non-Newtonian fluids.We use a matrix formulated algorithm to approximate solutions of a class of partial integro-differential equations with the given initial and boundary conditions. Some numerical results are presented to simplify application of operational matrix formulation and reduce the computational cost. Convergence analysis, error estimation and numerical stability of the method are also investigated. Finally, some test examples are given to demonstrate accuracy and efficiency of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Legendre%20Wavelets" title="Legendre Wavelets">Legendre Wavelets</a>, <a href="https://publications.waset.org/abstracts/search?q=operational%20matrices" title=" operational matrices"> operational matrices</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation" title=" partial integro-differential equation"> partial integro-differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=viscoelasticity" title=" viscoelasticity"> viscoelasticity</a> </p> <a href="https://publications.waset.org/abstracts/58007/development-of-a-model-based-on-wavelets-and-matrices-for-the-treatment-of-weakly-singular-partial-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58007.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">336</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4273</span> Application of a Modified Crank-Nicolson Method in Metallurgy</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kobamelo%20Mashaba">Kobamelo Mashaba</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The molten slag has a high substantial temperatures range between 1723-1923, carrying a huge amount of useful energy for reducing energy consumption and CO₂ emissions under the heat recovery process. Therefore in this study, we investigated the performance of the modified crank Nicolson method for a delayed partial differential equation on the heat recovery of molten slag in the metallurgical mining environment. It was proved that the proposed method converges quickly compared to the classic method with the existence of a unique solution. It was inferred from numerical result that the proposed methodology is more viable and profitable for the mining industry. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delayed%20partial%20differential%20equation" title="delayed partial differential equation">delayed partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=modified%20Crank-Nicolson%20Method" title=" modified Crank-Nicolson Method"> modified Crank-Nicolson Method</a>, <a href="https://publications.waset.org/abstracts/search?q=molten%20slag" title=" molten slag"> molten slag</a>, <a href="https://publications.waset.org/abstracts/search?q=heat%20recovery" title=" heat recovery"> heat recovery</a>, <a href="https://publications.waset.org/abstracts/search?q=parabolic%20equation" title=" parabolic equation"> parabolic equation</a> </p> <a href="https://publications.waset.org/abstracts/152073/application-of-a-modified-crank-nicolson-method-in-metallurgy" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/152073.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">101</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4272</span> Scrutiny and Solving Analytically Nonlinear Differential at Engineering Field of Fluids, Heat, Mass and Wave by New Method AGM</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammadreza%20Akbari">Mohammadreza Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Sara%20Akbari"> Sara Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Davood%20Domiri%20Ganji"> Davood Domiri Ganji</a>, <a href="https://publications.waset.org/abstracts/search?q=Pooya%20Solimani"> Pooya Solimani</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Khalili"> Reza Khalili</a> </p> <p class="card-text"><strong>Abstract:</strong></p> As all experts know most of engineering system behavior in practical are nonlinear process (especially heat, fluid and mass, etc.) and analytical solving (no numeric) these problems are difficult, complex and sometimes impossible like (fluids and gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure a innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will be emerged after comparing the achieved solutions by Numerical method (Runge-Kutte 4th) and so compare to other methods such as HPM, ADM,… and exact solutions. Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students (engineering and basic science) in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear differential equations, with help of that there is no difficulty for solving nonlinear differential equations(ODE and PDE). In this paper, we investigate and solve 4 types of the nonlinear differential equation with AGM method : 1-Heat and fluid, 2-Unsteady state of nonlinear partial differential, 3-Coupled nonlinear partial differential in wave equation, and 4-Nonlinear integro-differential equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=new%20method%20AGM" title="new method AGM">new method AGM</a>, <a href="https://publications.waset.org/abstracts/search?q=sets%20of%20coupled%20nonlinear%20equations%20at%20engineering%20field" title=" sets of coupled nonlinear equations at engineering field"> sets of coupled nonlinear equations at engineering field</a>, <a href="https://publications.waset.org/abstracts/search?q=waves%20equations" title=" waves equations"> waves equations</a>, <a href="https://publications.waset.org/abstracts/search?q=integro-differential" title=" integro-differential"> integro-differential</a>, <a href="https://publications.waset.org/abstracts/search?q=fluid%20and%20thermal" title=" fluid and thermal"> fluid and thermal</a> </p> <a href="https://publications.waset.org/abstracts/36022/scrutiny-and-solving-analytically-nonlinear-differential-at-engineering-field-of-fluids-heat-mass-and-wave-by-new-method-agm" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/36022.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">546</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4271</span> Closed Form Exact Solution for Second Order Linear Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Otarod">Saeed Otarod</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In a different simple and straight forward analysis a closed-form integral solution is found for nonhomogeneous second order linear ordinary differential equations, in terms of a particular solution of their corresponding homogeneous part. To find the particular solution of the homogeneous part, the equation is transformed into a simple Riccati equation from which the general solution of non-homogeneouecond order differential equation, in the form of a closed integral equation is inferred. The method works well in manyimportant cases, such as Schrödinger equation for hydrogen-like atoms. A non-homogenous second order linear differential equation has been solved as an extra example <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=explicit" title="explicit">explicit</a>, <a href="https://publications.waset.org/abstracts/search?q=linear" title=" linear"> linear</a>, <a href="https://publications.waset.org/abstracts/search?q=differential" title=" differential"> differential</a>, <a href="https://publications.waset.org/abstracts/search?q=closed%20form" title=" closed form"> closed form</a> </p> <a href="https://publications.waset.org/abstracts/185365/closed-form-exact-solution-for-second-order-linear-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/185365.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">63</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4270</span> The Data-Driven Localized Wave Solution of the Fokas-Lenells Equation using PINN</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia">Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta"> Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The physics informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary condition to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful to study various optical phenomena. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deep%20learning" title="deep learning">deep learning</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20Soliton" title=" optical Soliton"> optical Soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20network" title=" neural network"> neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/165868/the-data-driven-localized-wave-solution-of-the-fokas-lenells-equation-using-pinn" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165868.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">126</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4269</span> A Nonlinear Parabolic Partial Differential Equation Model for Image Enhancement</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Tudor%20Barbu">Tudor Barbu</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a robust nonlinear parabolic partial differential equation (PDE)-based denoising scheme in this article. Our approach is based on a second-order anisotropic diffusion model that is described first. Then, a consistent and explicit numerical approximation algorithm is constructed for this continuous model by using the finite-difference method. Finally, our restoration experiments and method comparison, which prove the effectiveness of this proposed technique, are discussed in this paper. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=anisotropic%20diffusion" title="anisotropic diffusion">anisotropic diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=finite%20differences" title=" finite differences"> finite differences</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20denoising%20and%20restoration" title=" image denoising and restoration"> image denoising and restoration</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20PDE%20model" title=" nonlinear PDE model"> nonlinear PDE model</a>, <a href="https://publications.waset.org/abstracts/search?q=anisotropic%20diffusion" title=" anisotropic diffusion"> anisotropic diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20approximation%20schemes" title=" numerical approximation schemes"> numerical approximation schemes</a> </p> <a href="https://publications.waset.org/abstracts/48289/a-nonlinear-parabolic-partial-differential-equation-model-for-image-enhancement" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/48289.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">313</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4268</span> A Trapezoidal-Like Integrator for the Numerical Solution of One-Dimensional Time Dependent Schrödinger Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Johnson%20Oladele%20Fatokun">Johnson Oladele Fatokun</a>, <a href="https://publications.waset.org/abstracts/search?q=I.%20P.%20Akpan"> I. P. Akpan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the one-dimensional time dependent Schrödinger equation is discretized by the method of lines using a second order finite difference approximation to replace the second order spatial derivative. The evolving system of stiff ordinary differential equation (ODE) in time is solved numerically by an L-stable trapezoidal-like integrator. Results show accuracy of relative maximum error of order 10-4 in the interval of consideration. The performance of the method as compared to an existing scheme is considered favorable. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Schrodinger%E2%80%99s%20equation" title="Schrodinger’s equation">Schrodinger’s equation</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations" title=" partial differential equations"> partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=method%20of%20lines%20%28MOL%29" title=" method of lines (MOL)"> method of lines (MOL)</a>, <a href="https://publications.waset.org/abstracts/search?q=stiff%20ODE" title=" stiff ODE"> stiff ODE</a>, <a href="https://publications.waset.org/abstracts/search?q=trapezoidal-like%20integrator" title=" trapezoidal-like integrator "> trapezoidal-like integrator </a> </p> <a href="https://publications.waset.org/abstracts/11665/a-trapezoidal-like-integrator-for-the-numerical-solution-of-one-dimensional-time-dependent-schrodinger-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/11665.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">418</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4267</span> The Data-Driven Localized Wave Solution of the Fokas-Lenells Equation Using Physics-Informed Neural Network</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Gautam%20Kumar%20Saharia">Gautam Kumar Saharia</a>, <a href="https://publications.waset.org/abstracts/search?q=Sagardeep%20Talukdar"> Sagardeep Talukdar</a>, <a href="https://publications.waset.org/abstracts/search?q=Riki%20Dutta"> Riki Dutta</a>, <a href="https://publications.waset.org/abstracts/search?q=Sudipta%20Nandy"> Sudipta Nandy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The physics-informed neural network (PINN) method opens up an approach for numerically solving nonlinear partial differential equations leveraging fast calculating speed and high precession of modern computing systems. We construct the PINN based on a strong universal approximation theorem and apply the initial-boundary value data and residual collocation points to weekly impose initial and boundary conditions to the neural network and choose the optimization algorithms adaptive moment estimation (ADAM) and Limited-memory Broyden-Fletcher-Golfard-Shanno (L-BFGS) algorithm to optimize learnable parameter of the neural network. Next, we improve the PINN with a weighted loss function to obtain both the bright and dark soliton solutions of the Fokas-Lenells equation (FLE). We find the proposed scheme of adjustable weight coefficients into PINN has a better convergence rate and generalizability than the basic PINN algorithm. We believe that the PINN approach to solve the partial differential equation appearing in nonlinear optics would be useful in studying various optical phenomena. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=deep%20learning" title="deep learning">deep learning</a>, <a href="https://publications.waset.org/abstracts/search?q=optical%20soliton" title=" optical soliton"> optical soliton</a>, <a href="https://publications.waset.org/abstracts/search?q=physics%20informed%20neural%20network" title=" physics informed neural network"> physics informed neural network</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/165242/the-data-driven-localized-wave-solution-of-the-fokas-lenells-equation-using-physics-informed-neural-network" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/165242.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">70</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4266</span> A Mathematical-Based Formulation of EEG Fluctuations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Razi%20Khalafi">Razi Khalafi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Brain is the information processing center of the human body. Stimuli in form of information are transferred to the brain and then brain makes the decision on how to respond to them. In this research we propose a new partial differential equation which analyses the EEG signals and make a relationship between the incoming stimuli and the brain response to them. In order to test the proposed model, a set of external stimuli applied to the model and the model’s outputs were checked versus the real EEG data. The results show that this model can model the EEG signal well. The proposed model is useful not only for modeling of the EEG signal in case external stimuli but it can be used for the modeling of brain response in case of internal stimuli. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Brain" title="Brain">Brain</a>, <a href="https://publications.waset.org/abstracts/search?q=stimuli" title=" stimuli"> stimuli</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equation" title=" partial differential equation"> partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=response" title=" response"> response</a>, <a href="https://publications.waset.org/abstracts/search?q=eeg%20signal" title=" eeg signal"> eeg signal</a> </p> <a href="https://publications.waset.org/abstracts/30791/a-mathematical-based-formulation-of-eeg-fluctuations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/30791.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">433</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4265</span> Investigation a New Approach "AGM" to Solve of Complicate Nonlinear Partial Differential Equations at All Engineering Field and Basic Science</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mohammadreza%20Akbari">Mohammadreza Akbari</a>, <a href="https://publications.waset.org/abstracts/search?q=Pooya%20Soleimani%20Besheli"> Pooya Soleimani Besheli</a>, <a href="https://publications.waset.org/abstracts/search?q=Reza%20Khalili"> Reza Khalili</a>, <a href="https://publications.waset.org/abstracts/search?q=Davood%20Domiri%20Danji"> Davood Domiri Danji</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this conference, our aims are accuracy, capabilities and power at solving of the complicated non-linear partial differential. Our purpose is to enhance the ability to solve the mentioned nonlinear differential equations at basic science and engineering field and similar issues with a simple and innovative approach. As we know most of engineering system behavior in practical are nonlinear process (especially basic science and engineering field, etc.) and analytical solving (no numeric) these problems are difficult, complex, and sometimes impossible like (Fluids and Gas wave, these problems can't solve with numeric method, because of no have boundary condition) accordingly in this symposium we are going to exposure an innovative approach which we have named it Akbari-Ganji's Method or AGM in engineering, that can solve sets of coupled nonlinear differential equations (ODE, PDE) with high accuracy and simple solution and so this issue will emerge after comparing the achieved solutions by Numerical method (Runge-Kutta 4th). Eventually, AGM method will be proved that could be created huge evolution for researchers, professors and students in whole over the world, because of AGM coding system, so by using this software we can analytically solve all complicated linear and nonlinear partial differential equations, with help of that there is no difficulty for solving all nonlinear differential equations. Advantages and ability of this method (AGM) as follow: (a) Non-linear Differential equations (ODE, PDE) are directly solvable by this method. (b) In this method (AGM), most of the time, without any dimensionless procedure, we can solve equation(s) by any boundary or initial condition number. (c) AGM method always is convergent in boundary or initial condition. (d) Parameters of exponential, Trigonometric and Logarithmic of the existent in the non-linear differential equation with AGM method no needs Taylor expand which are caused high solve precision. (e) AGM method is very flexible in the coding system, and can solve easily varieties of the non-linear differential equation at high acceptable accuracy. (f) One of the important advantages of this method is analytical solving with high accuracy such as partial differential equation in vibration in solids, waves in water and gas, with minimum initial and boundary condition capable to solve problem. (g) It is very important to present a general and simple approach for solving most problems of the differential equations with high non-linearity in engineering sciences especially at civil engineering, and compare output with numerical method (Runge-Kutta 4th) and Exact solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=new%20approach" title="new approach">new approach</a>, <a href="https://publications.waset.org/abstracts/search?q=AGM" title=" AGM"> AGM</a>, <a href="https://publications.waset.org/abstracts/search?q=sets%20of%20coupled%20nonlinear%20differential%20equation" title=" sets of coupled nonlinear differential equation"> sets of coupled nonlinear differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical" title=" numerical"> numerical</a> </p> <a href="https://publications.waset.org/abstracts/32459/investigation-a-new-approach-agm-to-solve-of-complicate-nonlinear-partial-differential-equations-at-all-engineering-field-and-basic-science" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/32459.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">463</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4264</span> The Application of Variable Coefficient Jacobian elliptic Function Method to Differential-Difference Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chao-Qing%20Dai">Chao-Qing Dai</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In modern nonlinear science and textile engineering, nonlinear differential-difference equations are often used to describe some nonlinear phenomena. In this paper, we extend the variable coefficient Jacobian elliptic function method, which was used to find new exact travelling wave solutions of nonlinear partial differential equations, to nonlinear differential-difference equations. As illustration, we derive two series of Jacobian elliptic function solutions of the discrete sine-Gordon equation. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=discrete%20sine-Gordon%20equation" title="discrete sine-Gordon equation">discrete sine-Gordon equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient%20Jacobian%20elliptic%20function%20method" title=" variable coefficient Jacobian elliptic function method"> variable coefficient Jacobian elliptic function method</a>, <a href="https://publications.waset.org/abstracts/search?q=exact%20solutions" title=" exact solutions"> exact solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=equation" title=" equation"> equation</a> </p> <a href="https://publications.waset.org/abstracts/12987/the-application-of-variable-coefficient-jacobian-elliptic-function-method-to-differential-difference-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/12987.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">668</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4263</span> Reduced Differential Transform Methods for Solving the Fractional Diffusion Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Yildiray%20Keskin">Yildiray Keskin</a>, <a href="https://publications.waset.org/abstracts/search?q=Omer%20Acan"> Omer Acan</a>, <a href="https://publications.waset.org/abstracts/search?q=Murat%20Akkus"> Murat Akkus</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, the solution of fractional diffusion equations is presented by means of the reduced differential transform method. Fractional partial differential equations have special importance in engineering and sciences. Application of reduced differential transform method to this problem shows the rapid convergence of the sequence constructed by this method to the exact solution. The numerical results show that the approach is easy to implement and accurate when applied to fractional diffusion equations. The method introduces a promising tool for solving many fractional partial differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20diffusion%20equations" title="fractional diffusion equations">fractional diffusion equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Caputo%20fractional%20derivative" title=" Caputo fractional derivative"> Caputo fractional derivative</a>, <a href="https://publications.waset.org/abstracts/search?q=reduced%20differential%20transform%20method" title=" reduced differential transform method"> reduced differential transform method</a>, <a href="https://publications.waset.org/abstracts/search?q=partial" title=" partial"> partial</a> </p> <a href="https://publications.waset.org/abstracts/17526/reduced-differential-transform-methods-for-solving-the-fractional-diffusion-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/17526.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">525</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4262</span> Basket Option Pricing under Jump Diffusion Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ali%20Safdari-Vaighani">Ali Safdari-Vaighani</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Pricing financial contracts on several underlying assets received more and more interest as a demand for complex derivatives. The option pricing under asset price involving jump diffusion processes leads to the partial integral differential equation (PIDEs), which is an extension of the Black-Scholes PDE with a new integral term. The aim of this paper is to show how basket option prices in the jump diffusion models, mainly on the Merton model, can be computed using RBF based approximation methods. For a test problem, the RBF-PU method is applied for numerical solution of partial integral differential equation arising from the two-asset European vanilla put options. The numerical result shows the accuracy and efficiency of the presented method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=basket%20option" title="basket option">basket option</a>, <a href="https://publications.waset.org/abstracts/search?q=jump%20diffusion" title=" jump diffusion"> jump diffusion</a>, <a href="https://publications.waset.org/abstracts/search?q=%E2%80%8Eradial%20basis%20function" title=" ‎radial basis function"> ‎radial basis function</a>, <a href="https://publications.waset.org/abstracts/search?q=RBF-PUM" title=" RBF-PUM"> RBF-PUM</a> </p> <a href="https://publications.waset.org/abstracts/67152/basket-option-pricing-under-jump-diffusion-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/67152.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">354</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4261</span> Existence and Concentration of Solutions for a Class of Elliptic Partial Differential Equations Involving p-Biharmonic Operator</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Debajyoti%20Choudhuri">Debajyoti Choudhuri</a>, <a href="https://publications.waset.org/abstracts/search?q=Ratan%20Kumar%20Giri"> Ratan Kumar Giri</a>, <a href="https://publications.waset.org/abstracts/search?q=Shesadev%20Pradhan"> Shesadev Pradhan</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The perturbed nonlinear Schrodinger equation involving the p-biharmonic and the p-Laplacian operators involving a real valued parameter and a continuous real valued potential function defined over the N- dimensional Euclidean space has been considered. By the variational technique, an existence result pertaining to a nontrivial solution to this non-linear partial differential equation has been proposed. Further, by the Concentration lemma, the concentration of solutions to the same problem defined on the set consisting of those elements where the potential function vanishes as the real parameter approaches to infinity has been addressed. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=p-Laplacian" title="p-Laplacian">p-Laplacian</a>, <a href="https://publications.waset.org/abstracts/search?q=p-biharmonic" title=" p-biharmonic"> p-biharmonic</a>, <a href="https://publications.waset.org/abstracts/search?q=elliptic%20PDEs" title=" elliptic PDEs"> elliptic PDEs</a>, <a href="https://publications.waset.org/abstracts/search?q=Concentration%20lemma" title=" Concentration lemma"> Concentration lemma</a>, <a href="https://publications.waset.org/abstracts/search?q=Sobolev%20space" title=" Sobolev space"> Sobolev space</a> </p> <a href="https://publications.waset.org/abstracts/58393/existence-and-concentration-of-solutions-for-a-class-of-elliptic-partial-differential-equations-involving-p-biharmonic-operator" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/58393.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">236</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4260</span> Finite Element Method for Solving the Generalized RLW Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Abdel-Maksoud%20Abdel-Kader%20Soliman">Abdel-Maksoud Abdel-Kader Soliman</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The General Regularized Long Wave (GRLW) equation is solved numerically by giving a new algorithm based on collocation method using quartic B-splines at the mid-knot points as element shape. Also, we use the Fourth Runge-Kutta method for solving the system of first order ordinary differential equations instead of finite difference method. Our test problems, including the migration and interaction of solitary waves, are used to validate the algorithm which is found to be accurate and efficient. The three invariants of the motion are evaluated to determine the conservation properties of the algorithm. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=generalized%20RLW%20equation" title="generalized RLW equation">generalized RLW equation</a>, <a href="https://publications.waset.org/abstracts/search?q=solitons" title=" solitons"> solitons</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20b-spline" title=" quartic b-spline"> quartic b-spline</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equations" title=" nonlinear partial differential equations"> nonlinear partial differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=difference%20equations" title=" difference equations"> difference equations</a> </p> <a href="https://publications.waset.org/abstracts/9023/finite-element-method-for-solving-the-generalized-rlw-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/9023.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">489</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4259</span> Periodicity of Solutions of a Nonlinear Impulsive Differential Equation with Piecewise Constant Arguments</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mehtap%20Lafc%C4%B1">Mehtap Lafcı</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In recent years, oscillation, periodicity and convergence of solutions of linear differential equations with piecewise constant arguments have been significantly considered but there are only a few papers for impulsive differential equations with piecewise constant arguments. In this paper, a first order nonlinear impulsive differential equation with piecewise constant arguments is studied and the existence of solutions and periodic solutions of this equation are investigated by using Carvalho’s method. Finally, an example is given to illustrate these results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Carvalho%27s%20method" title="Carvalho's method">Carvalho's method</a>, <a href="https://publications.waset.org/abstracts/search?q=impulsive%20differential%20equation" title=" impulsive differential equation"> impulsive differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=periodic%20solution" title=" periodic solution"> periodic solution</a>, <a href="https://publications.waset.org/abstracts/search?q=piecewise%20constant%20arguments" title=" piecewise constant arguments"> piecewise constant arguments</a> </p> <a href="https://publications.waset.org/abstracts/33745/periodicity-of-solutions-of-a-nonlinear-impulsive-differential-equation-with-piecewise-constant-arguments" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/33745.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">515</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4258</span> A Nonstandard Finite Difference Method for Weather Derivatives Pricing Model</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Clarinda%20Vitorino%20Nhangumbe">Clarinda Vitorino Nhangumbe</a>, <a href="https://publications.waset.org/abstracts/search?q=Fredericks%20Ebrahim"> Fredericks Ebrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Betuel%20Canhanga"> Betuel Canhanga</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The price of an option weather derivatives can be approximated as a solution of the two-dimensional convection-diffusion dominant partial differential equation derived from the Ornstein-Uhlenbeck process, where one variable represents the weather dynamics and the other variable represent the underlying weather index. With appropriate financial boundary conditions, the solution of the pricing equation is approximated using a nonstandard finite difference method. It is shown that the proposed numerical scheme preserves positivity as well as stability and consistency. In order to illustrate the accuracy of the method, the numerical results are compared with other methods. The model is tested for real weather data. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=nonstandard%20finite%20differences" title="nonstandard finite differences">nonstandard finite differences</a>, <a href="https://publications.waset.org/abstracts/search?q=Ornstein-Uhlenbeck%20process" title=" Ornstein-Uhlenbeck process"> Ornstein-Uhlenbeck process</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20differential%20equations%20approach" title=" partial differential equations approach"> partial differential equations approach</a>, <a href="https://publications.waset.org/abstracts/search?q=weather%20derivatives" title=" weather derivatives"> weather derivatives</a> </p> <a href="https://publications.waset.org/abstracts/169730/a-nonstandard-finite-difference-method-for-weather-derivatives-pricing-model" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/169730.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> Downloads <span class="badge badge-light">110</span> </span> </div> </div> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4257</span> Quintic Spline Method for Variable Coefficient Fourth-Order Parabolic Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Reza%20Mohammadi">Reza Mohammadi</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahdieh%20Sahebi"> Mahdieh Sahebi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We develop a method based on polynomial quintic spline for numerical solution of fourth-order non-homogeneous parabolic partial differential equation with variable coefficient. By using polynomial quintic spline in off-step points in space and finite difference in time directions, we obtained two three level implicit methods. Stability analysis of the presented method has been carried out. We solve four test problems numerically to validate the proposed derived method. Numerical comparison with other existence methods shows the superiority of our presented scheme. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fourth-order%20parabolic%20equation" title="fourth-order parabolic equation">fourth-order parabolic equation</a>, <a href="https://publications.waset.org/abstracts/search?q=variable%20coefficient" title=" variable coefficient"> variable coefficient</a>, <a href="https://publications.waset.org/abstracts/search?q=polynomial%20quintic%20spline" title=" polynomial quintic spline"> polynomial quintic spline</a>, <a href="https://publications.waset.org/abstracts/search?q=off-step%20points" title=" off-step points"> off-step points</a>, <a href="https://publications.waset.org/abstracts/search?q=stability%20analysis" title=" stability analysis"> stability analysis</a> </p> <a 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