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Search results for: partial integro-differential equation
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class="card"> <div class="card-body"><strong>Paper Count:</strong> 3058</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: partial integro-differential equation</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">3058</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">3057</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">3056</span> A Study on Approximate Controllability of Impulsive Integrodifferential Systems with Non Local Conditions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Anandhi%20Santhosh">Anandhi Santhosh</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In order to describe various real-world problems in physical and engineering sciences subject to abrupt changes at certain instants during the evolution process, impulsive differential equations has been used to describe the system model. In this article, the problem of approximate controllability for nonlinear impulsive integrodifferential equations with state-dependent delay is investigated. We study the approximate controllability for nonlinear impulsive integrodifferential system under the assumption that the corresponding linear control system is approximately controllable. Using methods of functional analysis and semigroup theory, sufficient conditions are formulated and proved. Finally, an example is provided to illustrate the proposed theory. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximate%20controllability" title="approximate controllability">approximate controllability</a>, <a href="https://publications.waset.org/abstracts/search?q=impulsive%20differential%20system" title=" impulsive differential system"> impulsive differential system</a>, <a href="https://publications.waset.org/abstracts/search?q=fixed%20point%20theorem" title=" fixed point theorem"> fixed point theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=state-dependent%20delay" title=" state-dependent delay"> state-dependent delay</a> </p> <a href="https://publications.waset.org/abstracts/34723/a-study-on-approximate-controllability-of-impulsive-integrodifferential-systems-with-non-local-conditions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/34723.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">383</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">3055</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">3054</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">3053</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">3052</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">3051</span> A Series Solution of Fuzzy Integro-Differential Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Maryam%20Mosleh">Maryam Mosleh</a>, <a href="https://publications.waset.org/abstracts/search?q=Mahmood%20Otadi"> Mahmood Otadi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The hybrid differential equations have a wide range of applications in science and engineering. In this paper, the homotopy analysis method (HAM) is applied to obtain the series solution of the hybrid differential equations. Using the homotopy analysis method, it is possible to find the exact solution or an approximate solution of the problem. Comparisons are made between improved predictor-corrector method, homotopy analysis method and the exact solution. Finally, we illustrate our approach by some numerical example. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuzzy%20number" title="Fuzzy number">Fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=parametric%20form%20of%20a%20fuzzy%20number" title=" parametric form of a fuzzy number"> parametric form of a fuzzy number</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20integrodifferential%20equation" title=" fuzzy integrodifferential equation"> fuzzy integrodifferential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=homotopy%20analysis%20method" title=" homotopy analysis method"> homotopy analysis method</a> </p> <a href="https://publications.waset.org/abstracts/31775/a-series-solution-of-fuzzy-integro-differential-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/31775.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">557</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">3050</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">3049</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">3048</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">3047</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">3046</span> Total Controllability of the Second Order Nonlinear Differential Equation with Delay and Non-Instantaneous Impulses</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Muslim%20Malik">Muslim Malik</a>, <a href="https://publications.waset.org/abstracts/search?q=Avadhesh%20Kumar"> Avadhesh Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A stronger concept of exact controllability which is called Total Controllability is introduced in this manuscript. Sufficient conditions have been established for the total controllability of a control problem, governed by second order nonlinear differential equation with delay and non-instantaneous impulses in a Banach space X. The results are obtained using the strongly continuous cosine family and Banach fixed point theorem. Also, the total controllability of an integrodifferential problem is investigated. At the end, some numerical examples are provided to illustrate the analytical findings. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Banach%20fixed%20point%20theorem" title="Banach fixed point theorem">Banach fixed point theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=non-instantaneous%20impulses" title=" non-instantaneous impulses"> non-instantaneous impulses</a>, <a href="https://publications.waset.org/abstracts/search?q=strongly%20continuous%20cosine%20family" title=" strongly continuous cosine family"> strongly continuous cosine family</a>, <a href="https://publications.waset.org/abstracts/search?q=total%20controllability" title=" total controllability"> total controllability</a> </p> <a href="https://publications.waset.org/abstracts/78296/total-controllability-of-the-second-order-nonlinear-differential-equation-with-delay-and-non-instantaneous-impulses" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/78296.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">298</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">3045</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">3044</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">3043</span> A Novel Method for Solving Nonlinear Whitham–Broer–Kaup Equation System</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ayda%20Nikkar">Ayda Nikkar</a>, <a href="https://publications.waset.org/abstracts/search?q=Roghayye%20Ahmadiasl"> Roghayye Ahmadiasl</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this letter, a new analytical method called homotopy perturbation method, which does not need small parameter in the equation is implemented for solving the nonlinear Whitham–Broer–Kaup (WBK) partial differential equation. In this method, a homotopy is introduced to be constructed for the equation. The initial approximations can be freely chosen with possible unknown constants which can be determined by imposing the boundary and initial conditions. Comparison of the results with those of exact solution has led us to significant consequences. The results reveal that the HPM is very effective, convenient and quite accurate to systems of nonlinear equations. It is predicted that the HPM can be found widely applicable in engineering. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=homotopy%20perturbation%20method" title="homotopy perturbation method">homotopy perturbation method</a>, <a href="https://publications.waset.org/abstracts/search?q=Whitham%E2%80%93Broer%E2%80%93Kaup%20%28WBK%29%20equation" title=" Whitham–Broer–Kaup (WBK) equation"> Whitham–Broer–Kaup (WBK) equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Modified%20Boussinesq" title=" Modified Boussinesq"> Modified Boussinesq</a>, <a href="https://publications.waset.org/abstracts/search?q=Approximate%20Long%20Wave" title=" Approximate Long Wave"> Approximate Long Wave</a> </p> <a href="https://publications.waset.org/abstracts/35317/a-novel-method-for-solving-nonlinear-whitham-broer-kaup-equation-system" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/35317.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">311</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">3042</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">3041</span> Modeling of Nitrogen Solubility in Stainless Steel</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Saeed%20Ghali">Saeed Ghali</a>, <a href="https://publications.waset.org/abstracts/search?q=Hoda%20El-Faramawy"> Hoda El-Faramawy</a>, <a href="https://publications.waset.org/abstracts/search?q=Mamdouh%20Eissa"> Mamdouh Eissa</a>, <a href="https://publications.waset.org/abstracts/search?q=Michael%20Mishreky"> Michael Mishreky</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Scale-resistant austenitic stainless steel, X45CrNiW 18-9, has been developed, and modified steels produced through partial and total nickel replacement by nitrogen. These modified steels were produced in a 10 kg induction furnace under different nitrogen pressures and were cast into ingots. The produced modified stainless steels were forged, followed by air cooling. The phases of modified stainless steels have been investigated using the Schaeffler diagram, dilatometer, and microstructure observations. Both partial and total replacement of nickel using 0.33-0.50% nitrogen are effective in producing fully austenitic stainless steels. The nitrogen contents were determined and compared with those calculated using the Institute of Metal Science (IMS) equation. The results showed great deviations between the actual nitrogen contents and predicted values through IMS equation. So, an equation has been derived based on chemical composition, pressure, and temperature at 1600oC. [N%] = 0.0078 + 0.0406*X, where X is a function of chemical composition and nitrogen pressure. The derived equation has been used to calculate the nitrogen content of different steels using published data. The results reveal the difficulty of deriving a general equation for the prediction of nitrogen content covering different steel compositions. So, it is necessary to use a narrow composition range. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=solubility" title="solubility">solubility</a>, <a href="https://publications.waset.org/abstracts/search?q=nitrogen" title=" nitrogen"> nitrogen</a>, <a href="https://publications.waset.org/abstracts/search?q=stainless%20steel" title=" stainless steel"> stainless steel</a>, <a href="https://publications.waset.org/abstracts/search?q=Schaeffler" title=" Schaeffler"> Schaeffler</a> </p> <a href="https://publications.waset.org/abstracts/155322/modeling-of-nitrogen-solubility-in-stainless-steel" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/155322.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">238</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">3040</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">3039</span> Operational Matrix Method for Fuzzy Fractional Reaction Diffusion Equation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Sachin%20Kumar">Sachin Kumar</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Fuzzy fractional diffusion equation is widely useful to depict different physical processes arising in physics, biology, and hydrology. The motive of this article is to deal with the fuzzy fractional diffusion equation. We study a mathematical model of fuzzy space-time fractional diffusion equation in which unknown function, coefficients, and initial-boundary conditions are fuzzy numbers. First, we find out a fuzzy operational matrix of Legendre polynomial of Caputo type fuzzy fractional derivative having a non-singular Mittag-Leffler kernel. The main advantages of this method are that it reduces the fuzzy fractional partial differential equation (FFPDE) to a system of fuzzy algebraic equations from which we can find the solution of the problem. The feasibility of our approach is shown by some numerical examples. Hence, our method is suitable to deal with FFPDE and has good accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=fractional%20PDE" title="fractional PDE">fractional PDE</a>, <a href="https://publications.waset.org/abstracts/search?q=fuzzy%20valued%20function" title=" fuzzy valued function"> fuzzy valued function</a>, <a href="https://publications.waset.org/abstracts/search?q=diffusion%20equation" title=" diffusion equation"> diffusion equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Legendre%20polynomial" title=" Legendre polynomial"> Legendre polynomial</a>, <a href="https://publications.waset.org/abstracts/search?q=spectral%20method" title=" spectral method"> spectral method</a> </p> <a href="https://publications.waset.org/abstracts/125273/operational-matrix-method-for-fuzzy-fractional-reaction-diffusion-equation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/125273.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">201</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">3038</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">3037</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">3036</span> Study on the Central Differencing Scheme with the Staggered Version (STG) for Solving the Hyperbolic Partial Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Narumol%20Chintaganun">Narumol Chintaganun</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper we present the second-order central differencing scheme with the staggered version (STG) for solving the advection equation and Burger's equation. This scheme based on staggered evolution of the re-constructed cell averages. This scheme results in the second-order central differencing scheme, an extension along the lines of the first-order central scheme of Lax-Friedrichs (LxF) scheme. All numerical simulations presented in this paper are obtained by finite difference method (FDM) and STG. Numerical results are shown that the STG gives very good results and higher accuracy. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=central%20differencing%20scheme" title="central differencing scheme">central differencing scheme</a>, <a href="https://publications.waset.org/abstracts/search?q=STG" title=" STG"> STG</a>, <a href="https://publications.waset.org/abstracts/search?q=advection%20equation" title=" advection equation"> advection equation</a>, <a href="https://publications.waset.org/abstracts/search?q=burgers%20equation" title=" burgers equation"> burgers equation</a> </p> <a href="https://publications.waset.org/abstracts/23076/study-on-the-central-differencing-scheme-with-the-staggered-version-stg-for-solving-the-hyperbolic-partial-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/23076.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">557</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">3035</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">3034</span> The Construction of Exact Solutions for the Nonlinear Lattice Equation via Coth and Csch Functions Method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20Zerarka">A. Zerarka</a>, <a href="https://publications.waset.org/abstracts/search?q=W.%20Djoudi"> W. Djoudi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The method developed in this work uses a generalised coth and csch funtions method to construct new exact travelling solutions to the nonlinear lattice equation. The technique of the homogeneous balance method is used to handle the appropriated solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=coth%20functions" title="coth functions">coth functions</a>, <a href="https://publications.waset.org/abstracts/search?q=csch%20functions" title=" csch functions"> csch functions</a>, <a href="https://publications.waset.org/abstracts/search?q=nonlinear%20partial%20differential%20equation" title=" nonlinear partial differential equation"> nonlinear partial differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=travelling%20wave%20solutions" title=" travelling wave solutions"> travelling wave solutions</a> </p> <a href="https://publications.waset.org/abstracts/20374/the-construction-of-exact-solutions-for-the-nonlinear-lattice-equation-via-coth-and-csch-functions-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20374.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">663</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">3033</span> Volumetric Properties of Binary Mixtures of Glycerol +1-Butanol or +2-Butanol at Several Temperatures</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20Chabouni">Y. Chabouni</a>, <a href="https://publications.waset.org/abstracts/search?q=F.%20Amireche"> F. Amireche</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Densities of glycerol + 1-butanol or 2-butanol mixtures were measured over the temperature range 293.15 to 303.15 K at atmospheric pressure, over the entire composition range, with a vibrating tube densimeter. Excess molar volumes, apparent and partial molar volumes of glycerol and butanol, thermal isobaric expansivities of the mixture and partial molar expansivities of the components were calculated. The excess molar volumes of the mixtures are negative at all temperatures, and deviations from ideality increase with increasing temperature. Excess molar volumes were fitted to the Redlich–Kister equation. Partial molar volumes of glycerol decrease with increasing butanol concentration. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=1-Butanol" title="1-Butanol">1-Butanol</a>, <a href="https://publications.waset.org/abstracts/search?q=2-Butanol" title=" 2-Butanol"> 2-Butanol</a>, <a href="https://publications.waset.org/abstracts/search?q=density" title=" density"> density</a>, <a href="https://publications.waset.org/abstracts/search?q=excess%20molar%20volume" title=" excess molar volume"> excess molar volume</a>, <a href="https://publications.waset.org/abstracts/search?q=glycerol" title=" glycerol"> glycerol</a>, <a href="https://publications.waset.org/abstracts/search?q=partial%20molar%20property" title=" partial molar property"> partial molar property</a>, <a href="https://publications.waset.org/abstracts/search?q=thermal%20isobaric%20expansivities" title=" thermal isobaric expansivities"> thermal isobaric expansivities</a> </p> <a href="https://publications.waset.org/abstracts/80077/volumetric-properties-of-binary-mixtures-of-glycerol-1-butanol-or-2-butanol-at-several-temperatures" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/80077.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">190</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">3032</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">3031</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">3030</span> A New Computational Method for the Solution of Nonlinear Burgers' Equation Arising in Longitudinal Dispersion Phenomena in Fluid Flow through Porous Media</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Olayiwola%20Moruf%20Oyedunsi">Olayiwola Moruf Oyedunsi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper discusses the Modified Variational Iteration Method (MVIM) for the solution of nonlinear Burgers’ equation arising in longitudinal dispersion phenomena in fluid flow through porous media. The method is an elegant combination of Taylor’s series and the variational iteration method (VIM). Using Maple 18 for implementation, it is observed that the procedure provides rapidly convergent approximation with less computational efforts. The result shows that the concentration C(x,t) of the contaminated water decreases as distance x increases for the given time t. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=modified%20variational%20iteration%20method" title="modified variational iteration method">modified variational iteration method</a>, <a href="https://publications.waset.org/abstracts/search?q=Burger%E2%80%99s%20equation" title=" Burger’s equation"> Burger’s equation</a>, <a href="https://publications.waset.org/abstracts/search?q=porous%20media" title=" porous media"> porous media</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/44343/a-new-computational-method-for-the-solution-of-nonlinear-burgers-equation-arising-in-longitudinal-dispersion-phenomena-in-fluid-flow-through-porous-media" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/44343.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">321</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">3029</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> <ul class="pagination"> <li class="page-item disabled"><span class="page-link">‹</span></li> <li class="page-item active"><span class="page-link">1</span></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation&page=2">2</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation&page=3">3</a></li> <li class="page-item"><a class="page-link" href="https://publications.waset.org/abstracts/search?q=partial%20integro-differential%20equation&page=4">4</a></li> <li class="page-item"><a class="page-link" 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