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delay differential equations</title> <meta name="description" content="Search results for: stochastic delay differential equations"> <meta name="keywords" content="stochastic delay differential equations"> <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 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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="stochastic delay differential equations"> <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> 4145</div> </div> </div> </div> <h1 class="mt-3 mb-3 text-center" style="font-size:1.6rem;">Search results for: stochastic delay differential equations</h1> <div class="card paper-listing mb-3 mt-3"> <h5 class="card-header" style="font-size:.9rem"><span class="badge badge-info">4145</span> Weak Solutions Of Stochastic Fractional Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Lev%20Idels">Lev Idels</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Stochastic fractional differential equations have recently attracted considerable attention, as they have been used to model real-world processes, which are subject to natural memory effects and measurement uncertainties. Compared to conventional hereditary differential equations, one of the advantages of fractional differential equations is related to more realistic geometric properties of their trajectories that do not intersect in the phase space. In this report, a Peano-like existence theorem for nonlinear stochastic fractional differential equations is proven under very general hypotheses. Several specific classes of equations are checked to satisfy these hypotheses, including delay equations driven by the fractional Brownian motion, stochastic fractional neutral equations and many others. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title="delay equations">delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a>, <a href="https://publications.waset.org/abstracts/search?q=weak%20solutions" title=" weak solutions"> weak solutions</a> </p> <a href="https://publications.waset.org/abstracts/146592/weak-solutions-of-stochastic-fractional-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/146592.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">209</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">4144</span> Stochastic Age-Structured Population Models</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Many well-known age-structured population models are derived from the celebrated McKendrick-von Foerster equation (MFE), also called the biological conservation law. A similar technique is suggested for the stochastically perturbed MFE. This technique is shown to produce stochastic versions of the deterministic population models, which appear to be very different from those one can construct by simply appending additive stochasticity to deterministic equations. In particular, it is shown that stochastic Nicholson’s blowflies model should contain both additive and multiplicative stochastic noises. The suggested transformation technique is similar to that used in the deterministic case. The difference is hidden in the formulas for the exact solutions of the simplified boundary value problem for the stochastically perturbed MFE. The analysis is also based on the theory of stochastic delay differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=boundary%20value%20problems" title="boundary value problems">boundary value problems</a>, <a href="https://publications.waset.org/abstracts/search?q=population%20models" title=" population models"> population models</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20delay%20differential%20equations" title=" stochastic delay differential equations"> stochastic delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20partial%20differential%20equation" title=" stochastic partial differential equation"> stochastic partial differential equation</a> </p> <a href="https://publications.waset.org/abstracts/138398/stochastic-age-structured-population-models" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/138398.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">254</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">4143</span> Lyapunov and Input-to-State Stability of Stochastic Differential Equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov">Arcady Ponosov</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Input-to-State Stability (ISS) is widely used in deterministic control theory but less known in the stochastic case. Roughly speaking, the theory explains when small perturbations of the right-hand sides of the system on the entire semiaxis cause only small changes in the solutions of the system, again on the entire semiaxis. This property is crucial in many applications. In the report, we explain how to define and study ISS for systems of linear stochastic differential equations with or without delays. The central result connects ISS with the property of Lyapunov stability. This relationship is well-known in the deterministic setting, but its stochastic version is new. As an application, a method of studying asymptotic Lyapunov stability for stochastic delay equations is described and justified. Several examples are provided that confirm the efficiency and simplicity of the framework. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20perturbations" title=" stochastic perturbations"> stochastic perturbations</a> </p> <a href="https://publications.waset.org/abstracts/127764/lyapunov-and-input-to-state-stability-of-stochastic-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/127764.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">176</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">4142</span> Sufficient Conditions for Exponential Stability of Stochastic Differential Equations with Non Trivial Solutions</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fakhreddin%20Abedi">Fakhreddin Abedi</a>, <a href="https://publications.waset.org/abstracts/search?q=Wah%20June%20Leong"> Wah June Leong</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Exponential stability of stochastic differential equations with non trivial solutions is provided in terms of Lyapunov functions. The main result of this paper establishes that, under certain hypotheses for the dynamics f(.) and g(.), practical exponential stability in probability at the small neighborhood of the origin is equivalent to the existence of an appropriate Lyapunov function. Indeed, we establish exponential stability of stochastic differential equation when almost all the state trajectories are bounded and approach a sufficiently small neighborhood of the origin. We derive sufficient conditions for exponential stability of stochastic differential equations. Finally, we give a numerical example illustrating our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=exponential%20stability%20in%20probability" title="exponential stability in probability">exponential stability in probability</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20technique" title=" Lyapunov technique"> Lyapunov technique</a>, <a href="https://publications.waset.org/abstracts/search?q=Ito%27s%20formula" title=" Ito's formula"> Ito's formula</a> </p> <a href="https://publications.waset.org/abstracts/184321/sufficient-conditions-for-exponential-stability-of-stochastic-differential-equations-with-non-trivial-solutions" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/184321.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">52</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">4141</span> Existence of positive periodic solutions for certain delay differential equations </h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Farid%20Nouioua">Farid Nouioua</a>, <a href="https://publications.waset.org/abstracts/search?q=Abdelouaheb%20Ardjouni"> Abdelouaheb Ardjouni</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this article, we study the existence of positive periodic solutions of certain delay differential equations. In the process we convert the differential equation into an equivalent integral equation after which appropriate mappings are constructed. We then employ Krasnoselskii's fixed point theorem to obtain sufficient conditions for the existence of a positive periodic solution of the differential equation. The obtained results improve and extend the results in the literature. Finally, an example is given to illustrate our results. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=delay%20differential%20equations" title="delay differential equations">delay differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=positive%20periodic%20solutions" title=" positive periodic solutions"> positive periodic solutions</a>, <a href="https://publications.waset.org/abstracts/search?q=integral%20equations" title=" integral equations"> integral equations</a>, <a href="https://publications.waset.org/abstracts/search?q=Krasnoselskii%20fixed%20point%20theorem" title=" Krasnoselskii fixed point theorem"> Krasnoselskii fixed point theorem</a> </p> <a href="https://publications.waset.org/abstracts/40904/existence-of-positive-periodic-solutions-for-certain-delay-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/40904.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">438</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">4140</span> Stochastic Variation of the Hubble's Parameter Using Ornstein-Uhlenbeck Process</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Mary%20Chriselda%20A">Mary Chriselda A</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper deals with the fact that the Hubble's parameter is not constant and tends to vary stochastically with time. This premise has been proven by converting it to a stochastic differential equation using the Ornstein-Uhlenbeck process. The formulated stochastic differential equation is further solved analytically using the Euler and the Kolmogorov Forward equations, thereby obtaining the probability density function using the Fourier transformation, thereby proving that the Hubble's parameter varies stochastically. This is further corroborated by simulating the observations using Python and R-software for validation of the premise postulated. We can further draw conclusion that the randomness in forces affecting the white noise can eventually affect the Hubble’s Parameter leading to scale invariance and thereby causing stochastic fluctuations in the density and the rate of expansion of the Universe. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Chapman%20Kolmogorov%20forward%20differential%20equations" title="Chapman Kolmogorov forward differential equations">Chapman Kolmogorov forward differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=fourier%20transformation" title=" fourier transformation"> fourier transformation</a>, <a href="https://publications.waset.org/abstracts/search?q=hubble%27s%20parameter" title=" hubble's parameter"> hubble's parameter</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=stochastic%20differential%20equations" title=" stochastic differential equations "> stochastic differential equations </a> </p> <a href="https://publications.waset.org/abstracts/116444/stochastic-variation-of-the-hubbles-parameter-using-ornstein-uhlenbeck-process" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/116444.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">4139</span> Global Stability Of Nonlinear Itô Equations And N. V. Azbelev's W-method</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov.">Arcady Ponosov.</a>, <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20Kadiev"> Ramazan Kadiev</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The work studies the global moment stability of solutions of systems of nonlinear differential Itô equations with delays. A modified regularization method (W-method) for the analysis of various types of stability of such systems, based on the choice of the auxiliaryequations and applications of the theory of positive invertible matrices, is proposed and justified. Development of this method for deterministic functional differential equations is due to N.V. Azbelev and his students. Sufficient conditions for the moment stability of solutions in terms of the coefficients for sufficiently general as well as specific classes of Itô equations are given. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=asymptotic%20stability" title="asymptotic stability">asymptotic stability</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20equations" title=" delay equations"> delay equations</a>, <a href="https://publications.waset.org/abstracts/search?q=operator%20methods" title=" operator methods"> operator methods</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20noise" title=" stochastic noise"> stochastic noise</a> </p> <a href="https://publications.waset.org/abstracts/143260/global-stability-of-nonlinear-ito-equations-and-n-v-azbelevs-w-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143260.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">224</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">4138</span> Modelling Structural Breaks in Stock Price Time Series Using Stochastic Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Daniil%20Karzanov">Daniil Karzanov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper studies the effect of quarterly earnings reports on the stock price. The profitability of the stock is modeled by geometric Brownian diffusion and the Constant Elasticity of Variance model. We fit several variations of stochastic differential equations to the pre-and after-report period using the Maximum Likelihood Estimation and Grid Search of parameters method. By examining the change in the model parameters after reports’ publication, the study reveals that the reports have enough evidence to be a structural breakpoint, meaning that all the forecast models exploited are not applicable for forecasting and should be refitted shortly. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=stock%20market" title="stock market">stock market</a>, <a href="https://publications.waset.org/abstracts/search?q=earnings%20reports" title=" earnings reports"> earnings reports</a>, <a href="https://publications.waset.org/abstracts/search?q=financial%20time%20series" title=" financial time series"> financial time series</a>, <a href="https://publications.waset.org/abstracts/search?q=structural%20breaks" title=" structural breaks"> structural breaks</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a> </p> <a href="https://publications.waset.org/abstracts/143167/modelling-structural-breaks-in-stock-price-time-series-using-stochastic-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/143167.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">205</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">4137</span> Solution of Singularly Perturbed Differential Difference Equations Using Liouville Green Transformation</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Y.%20N.%20Reddy">Y. N. Reddy</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The class of differential-difference equations which have characteristics of both classes, i.e., delay/advance and singularly perturbed behaviour is known as singularly perturbed differential-difference equations. The expression ‘positive shift’ and ‘negative shift’ are also used for ‘advance’ and ‘delay’ respectively. In general, an ordinary differential equation in which the highest order derivative is multiplied by a small positive parameter and containing at least one delay/advance is known as singularly perturbed differential-difference equation. Singularly perturbed differential-difference equations arise in the modelling of various practical phenomena in bioscience, engineering, control theory, specifically in variational problems, in describing the human pupil-light reflex, in a variety of models for physiological processes or diseases and first exit time problems in the modelling of the determination of expected time for the generation of action potential in nerve cells by random synaptic inputs in dendrites. In this paper, we envisage the use of Liouville Green Transformation to find the solution of singularly perturbed differential difference equations. First, using Taylor series, the given singularly perturbed differential difference equation is approximated by an asymptotically equivalent singularly perturbation problem. Then the Liouville Green Transformation is applied to get the solution. Several model examples are solved, and the results are compared with other methods. It is observed that the present method gives better approximate solutions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=difference%20equations" title="difference equations">difference equations</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbations" title=" singular perturbations"> singular perturbations</a>, <a href="https://publications.waset.org/abstracts/search?q=boundary%20layer" title=" boundary layer"> boundary layer</a> </p> <a href="https://publications.waset.org/abstracts/86176/solution-of-singularly-perturbed-differential-difference-equations-using-liouville-green-transformation" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/86176.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">199</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">4136</span> Step Method for Solving Nonlinear Two Delays Differential Equation in Parkinson’s Disease</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=H.%20N.%20Agiza">H. N. Agiza</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Sohaly"> M. A. Sohaly</a>, <a href="https://publications.waset.org/abstracts/search?q=M.%20A.%20Elfouly"> M. A. Elfouly</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs<em>.</em> <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Parkinson%27s%20disease" title="Parkinson's disease">Parkinson's disease</a>, <a href="https://publications.waset.org/abstracts/search?q=step%20method" title=" step method"> step method</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20differential%20equation" title=" delay differential equation"> delay differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=two%20delays" title=" two delays"> two delays</a> </p> <a href="https://publications.waset.org/abstracts/131976/step-method-for-solving-nonlinear-two-delays-differential-equation-in-parkinsons-disease" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/131976.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">205</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">4135</span> Regularization of Gene Regulatory Networks Perturbed by White Noise</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Ramazan%20I.%20Kadiev">Ramazan I. Kadiev</a>, <a href="https://publications.waset.org/abstracts/search?q=Arcady%20Ponosov"> Arcady Ponosov</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Mathematical models of gene regulatory networks can in many cases be described by ordinary differential equations with switching nonlinearities, where the initial value problem is ill-posed. Several regularization methods are known in the case of deterministic networks, but the presence of stochastic noise leads to several technical difficulties. In the presentation, it is proposed to apply the methods of the stochastic singular perturbation theory going back to Yu. Kabanov and Yu. Pergamentshchikov. This approach is used to regularize the above ill-posed problem, which, e.g., makes it possible to design stable numerical schemes. Several examples are provided in the presentation, which support the efficiency of the suggested analysis. The method can also be of interest in other fields of biomathematics, where differential equations contain switchings, e.g., in neural field models. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=ill-posed%20problems" title="ill-posed problems">ill-posed problems</a>, <a href="https://publications.waset.org/abstracts/search?q=singular%20perturbation%20analysis" title=" singular perturbation analysis"> singular perturbation analysis</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=switching%20nonlinearities" title=" switching nonlinearities"> switching nonlinearities</a> </p> <a href="https://publications.waset.org/abstracts/85883/regularization-of-gene-regulatory-networks-perturbed-by-white-noise" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/85883.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">194</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">4134</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">4133</span> Solving SPDEs by Least Squares Method</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> </p> <p class="card-text"><strong>Abstract:</strong></p> We present in this paper a useful strategy to solve stochastic partial differential equations (SPDEs) involving stochastic coefficients. Using the Wick-product of higher order and the Wiener-Itˆo chaos expansion, the SPDEs is reformulated as a large system of deterministic partial differential equations. To reduce the computational complexity of this system, we shall use a decomposition-coordination method. To obtain the chaos coefficients in the corresponding deterministic equations, we use a least square formulation. 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=least%20squares" title="least squares">least squares</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%20chaos%20expansion" title=" wiener chaos expansion"> wiener chaos expansion</a>, <a href="https://publications.waset.org/abstracts/search?q=gradient%20method" title=" gradient method"> gradient method</a> </p> <a href="https://publications.waset.org/abstracts/4074/solving-spdes-by-least-squares-method" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/4074.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">419</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">4132</span> Method to Find a ε-Optimal Control of Stochastic Differential Equation Driven by a Brownian Motion</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Francys%20Souza">Francys Souza</a>, <a href="https://publications.waset.org/abstracts/search?q=Alberto%20Ohashi"> Alberto Ohashi</a>, <a href="https://publications.waset.org/abstracts/search?q=Dorival%20Leao"> Dorival Leao</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a general solution for finding the ε-optimal controls for non-Markovian stochastic systems as stochastic differential equations driven by Brownian motion, which is a problem recognized as a difficult solution. The contribution appears in the development of mathematical tools to deal with modeling and control of non-Markovian systems, whose applicability in different areas is well known. The methodology used consists to discretize the problem through a random discretization. In this way, we transform an infinite dimensional problem in a finite dimensional, thereafter we use measurable selection arguments, to find a control on an explicit form for the discretized problem. Then, we prove the control found for the discretized problem is a ε-optimal control for the original problem. Our theory provides a concrete description of a rather general class, among the principals, we can highlight financial problems such as portfolio control, hedging, super-hedging, pairs-trading and others. Therefore, our main contribution is the development of a tool to explicitly the ε-optimal control for non-Markovian stochastic systems. The pathwise analysis was made through a random discretization jointly with measurable selection arguments, has provided us with a structure to transform an infinite dimensional problem into a finite dimensional. The theory is applied to stochastic control problems based on path-dependent stochastic differential equations, where both drift and diffusion components are controlled. We are able to explicitly show optimal control with our method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=dynamic%20programming%20equation" title="dynamic programming equation">dynamic programming equation</a>, <a href="https://publications.waset.org/abstracts/search?q=optimal%20control" title=" optimal control"> optimal control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20control" title=" stochastic control"> stochastic control</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equation" title=" stochastic differential equation"> stochastic differential equation</a> </p> <a href="https://publications.waset.org/abstracts/94746/method-to-find-a-e-optimal-control-of-stochastic-differential-equation-driven-by-a-brownian-motion" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/94746.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">188</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">4131</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">4130</span> Development of Extended Trapezoidal Method for Numerical Solution of Volterra Integro-Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fuziyah%20Ishak">Fuziyah Ishak</a>, <a href="https://publications.waset.org/abstracts/search?q=Siti%20Norazura%20Ahmad"> Siti Norazura Ahmad</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Volterra integro-differential equations appear in many models for real life phenomena. Since analytical solutions for this type of differential equations are hard and at times impossible to attain, engineers and scientists resort to numerical solutions that can be made as accurately as possible. Conventionally, numerical methods for ordinary differential equations are adapted to solve Volterra integro-differential equations. In this paper, numerical solution for solving Volterra integro-differential equation using extended trapezoidal method is described. Formulae for the integral and differential parts of the equation are presented. Numerical results show that the extended method is suitable for solving first order Volterra integro-differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=accuracy" title="accuracy">accuracy</a>, <a href="https://publications.waset.org/abstracts/search?q=extended%20trapezoidal%20method" title=" extended trapezoidal method"> extended trapezoidal method</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20solution" title=" numerical solution"> numerical solution</a>, <a href="https://publications.waset.org/abstracts/search?q=Volterra%20integro-differential%20equations" title=" Volterra integro-differential equations"> Volterra integro-differential equations</a> </p> <a href="https://publications.waset.org/abstracts/52856/development-of-extended-trapezoidal-method-for-numerical-solution-of-volterra-integro-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52856.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">426</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">4129</span> Stability Analysis for an Extended Model of the Hypothalamus-Pituitary-Thyroid Axis</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Beata%20Jackowska-Zduniak">Beata Jackowska-Zduniak</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We formulate and analyze a mathematical model describing dynamics of the hypothalamus-pituitary-thyroid homoeostatic mechanism in endocrine system. We introduce to this system two types of couplings and delay. In our model, feedback controls the secretion of thyroid hormones and delay reflects time lags required for transportation of the hormones. The influence of delayed feedback on the stability behaviour of the system is discussed. Analytical results are illustrated by numerical examples of the model dynamics. This system of equations describes normal activity of the thyroid and also a couple of types of malfunctions (e.g. hyperthyroidism). <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=mathematical%20modeling" title="mathematical modeling">mathematical modeling</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=endocrine%20system" title=" endocrine system"> endocrine system</a>, <a href="https://publications.waset.org/abstracts/search?q=delay%20differential%20equation" title=" delay differential equation"> delay differential equation</a> </p> <a href="https://publications.waset.org/abstracts/52938/stability-analysis-for-an-extended-model-of-the-hypothalamus-pituitary-thyroid-axis" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/52938.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">4128</span> Hybrid Equity Warrants Pricing Formulation under Stochastic Dynamics</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Teh%20Raihana%20Nazirah%20Roslan">Teh Raihana Nazirah Roslan</a>, <a href="https://publications.waset.org/abstracts/search?q=Siti%20Zulaiha%20Ibrahim"> Siti Zulaiha Ibrahim</a>, <a href="https://publications.waset.org/abstracts/search?q=Sharmila%20Karim"> Sharmila Karim</a> </p> <p class="card-text"><strong>Abstract:</strong></p> A warrant is a financial contract that confers the right but not the obligation, to buy or sell a security at a certain price before expiration. The standard procedure to value equity warrants using call option pricing models such as the Black–Scholes model had been proven to contain many flaws, such as the assumption of constant interest rate and constant volatility. In fact, existing alternative models were found focusing more on demonstrating techniques for pricing, rather than empirical testing. Therefore, a mathematical model for pricing and analyzing equity warrants which comprises stochastic interest rate and stochastic volatility is essential to incorporate the dynamic relationships between the identified variables and illustrate the real market. Here, the aim is to develop dynamic pricing formulations for hybrid equity warrants by incorporating stochastic interest rates from the Cox-Ingersoll-Ross (CIR) model, along with stochastic volatility from the Heston model. The development of the model involves the derivations of stochastic differential equations that govern the model dynamics. The resulting equations which involve Cauchy problem and heat equations are then solved using partial differential equation approaches. The analytical pricing formulas obtained in this study comply with the form of analytical expressions embedded in the Black-Scholes model and other existing pricing models for equity warrants. This facilitates the practicality of this proposed formula for comparison purposes and further empirical study. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Cox-Ingersoll-Ross%20model" title="Cox-Ingersoll-Ross model">Cox-Ingersoll-Ross model</a>, <a href="https://publications.waset.org/abstracts/search?q=equity%20warrants" title=" equity warrants"> equity warrants</a>, <a href="https://publications.waset.org/abstracts/search?q=Heston%20model" title=" Heston model"> Heston model</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20models" title=" hybrid models"> hybrid models</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic" title=" stochastic"> stochastic</a> </p> <a href="https://publications.waset.org/abstracts/124157/hybrid-equity-warrants-pricing-formulation-under-stochastic-dynamics" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/124157.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">129</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">4127</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">4126</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">4125</span> A Nonlinear Stochastic Differential Equation Model for Financial Bubbles and Crashes with Finite-Time Singularities</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Haowen%20Xi">Haowen Xi</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We propose and solve exactly a class of non-linear generalization of the Black-Scholes process of stochastic differential equations describing price bubble and crashes dynamics. As a result of nonlinear positive feedback, the faster-than-exponential price positive growth (bubble forming) and negative price growth (crash forming) are found to be the power-law finite-time singularity in which bubbles and crashes price formation ending at finite critical time tc. While most literature on the market bubble and crash process focuses on the nonlinear positive feedback mechanism aspect, very few studies concern the noise level on the same process. The present work adds to the market bubble and crashes literature by studying the external sources noise influence on the critical time tc of the bubble forming and crashes forming. Two main results will be discussed: (1) the analytical expression of expected value of the critical time <tc> is found and unexpected critical slowing down due to the coupling external noise is predicted; (2) numerical simulations of the nonlinear stochastic equation is presented, and the probability distribution of Prob(tc) is found to be the inverse gamma function. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=bubble" title="bubble">bubble</a>, <a href="https://publications.waset.org/abstracts/search?q=crash" title=" crash"> crash</a>, <a href="https://publications.waset.org/abstracts/search?q=finite-time-singular" title=" finite-time-singular"> finite-time-singular</a>, <a href="https://publications.waset.org/abstracts/search?q=numerical%20simulation" title=" numerical simulation"> numerical simulation</a>, <a href="https://publications.waset.org/abstracts/search?q=price%20dynamics" title=" price dynamics"> price dynamics</a>, <a href="https://publications.waset.org/abstracts/search?q=stochastic%20differential%20equations" title=" stochastic differential equations"> stochastic differential equations</a> </p> <a href="https://publications.waset.org/abstracts/120932/a-nonlinear-stochastic-differential-equation-model-for-financial-bubbles-and-crashes-with-finite-time-singularities" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/120932.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">132</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">4124</span> Nonhomogeneous Linear Second Order Differential Equations and Resonance through Geogebra Program</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=F.%20Maass">F. Maass</a>, <a href="https://publications.waset.org/abstracts/search?q=P.%20Martin"> P. Martin</a>, <a href="https://publications.waset.org/abstracts/search?q=J.%20Olivares"> J. Olivares</a> </p> <p class="card-text"><strong>Abstract:</strong></p> The aim of this work is the application of the program GeoGebra in teaching the study of nonhomogeneous linear second order differential equations with constant coefficients. Different kind of functions or forces will be considered in the right hand side of the differential equations, in particular, the emphasis will be placed in the case of trigonometrical functions producing the resonance phenomena. In order to obtain this, the frequencies of the trigonometrical functions will be changed. Once the resonances appear, these have to be correlationated with the roots of the second order algebraic equation determined by the coefficients of the differential equation. In this way, the physics and engineering students will understand resonance effects and its consequences in the simplest way. A large variety of examples will be shown, using different kind of functions for the nonhomogeneous part of the differential equations. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=education" title="education">education</a>, <a href="https://publications.waset.org/abstracts/search?q=geogebra" title=" geogebra"> geogebra</a>, <a href="https://publications.waset.org/abstracts/search?q=ordinary%20differential%20equations" title=" ordinary differential equations"> ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=resonance" title=" resonance"> resonance</a> </p> <a href="https://publications.waset.org/abstracts/90040/nonhomogeneous-linear-second-order-differential-equations-and-resonance-through-geogebra-program" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/90040.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">245</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">4123</span> Generalization of Tau Approximant and Error Estimate of Integral Form of Tau Methods for Some Class of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20I.%20Ma%E2%80%99ali">A. I. Ma’ali</a>, <a href="https://publications.waset.org/abstracts/search?q=R.%20B.%20Adeniyi"> R. B. Adeniyi</a>, <a href="https://publications.waset.org/abstracts/search?q=A.%20Y.%20Badeggi"> A. Y. Badeggi</a>, <a href="https://publications.waset.org/abstracts/search?q=U.%20Mohammed"> U. Mohammed </a> </p> <p class="card-text"><strong>Abstract:</strong></p> An error estimation of the integrated formulation of the Lanczos tau method for some class of ordinary differential equations was reported. This paper is concern with the generalization of tau approximants and their corresponding error estimates for some class of ordinary differential equations (ODEs) characterized by m + s =3 (i.e for m =1, s=2; m=2, s=1; and m=3, s=0) where m and s are the order of differential equations and number of overdetermination, respectively. The general result obtained were validated with some numerical examples. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=approximant" title="approximant">approximant</a>, <a href="https://publications.waset.org/abstracts/search?q=error%20estimate" title=" error estimate"> error estimate</a>, <a href="https://publications.waset.org/abstracts/search?q=tau%20method" title=" tau method"> tau method</a>, <a href="https://publications.waset.org/abstracts/search?q=overdetermination" title=" overdetermination"> overdetermination</a> </p> <a href="https://publications.waset.org/abstracts/16442/generalization-of-tau-approximant-and-error-estimate-of-integral-form-of-tau-methods-for-some-class-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/16442.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">606</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">4122</span> Dynamical Relation of Poisson Spike Trains in Hodkin-Huxley Neural Ion Current Model and Formation of Non-Canonical Bases, Islands, and Analog Bases in DNA, mRNA, and RNA at or near the Transcription</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Michael%20Fundator">Michael Fundator</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Groundbreaking application of biomathematical and biochemical research in neural networks processes to formation of non-canonical bases, islands, and analog bases in DNA and mRNA at or near the transcription that contradicts the long anticipated statistical assumptions for the distribution of bases and analog bases compounds is implemented through statistical and stochastic methods apparatus with addition of quantum principles, where the usual transience of Poisson spike train becomes very instrumental tool for finding even almost periodical type of solutions to Fokker-Plank stochastic differential equation. Present article develops new multidimensional methods of finding solutions to stochastic differential equations based on more rigorous approach to mathematical apparatus through Kolmogorov-Chentsov continuity theorem that allows the stochastic processes with jumps under certain conditions to have γ-Holder continuous modification that is used as basis for finding analogous parallels in dynamics of neutral networks and formation of analog bases and transcription in DNA. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=Fokker-Plank%20stochastic%20differential%20equation" title="Fokker-Plank stochastic differential equation">Fokker-Plank stochastic differential equation</a>, <a href="https://publications.waset.org/abstracts/search?q=Kolmogorov-Chentsov%20continuity%20theorem" title=" Kolmogorov-Chentsov continuity theorem"> Kolmogorov-Chentsov continuity theorem</a>, <a href="https://publications.waset.org/abstracts/search?q=neural%20networks" title=" neural networks"> neural networks</a>, <a href="https://publications.waset.org/abstracts/search?q=translation%20and%20transcription" title=" translation and transcription"> translation and transcription</a> </p> <a href="https://publications.waset.org/abstracts/130033/dynamical-relation-of-poisson-spike-trains-in-hodkin-huxley-neural-ion-current-model-and-formation-of-non-canonical-bases-islands-and-analog-bases-in-dna-mrna-and-rna-at-or-near-the-transcription" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/130033.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">406</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">4121</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">4120</span> Numerical Solution for Integro-Differential Equations by Using Quartic B-Spline Wavelet and Operational Matrices</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Khosrow%20Maleknejad">Khosrow Maleknejad</a>, <a href="https://publications.waset.org/abstracts/search?q=Yaser%20Rostami"> Yaser Rostami</a> </p> <p class="card-text"><strong>Abstract:</strong></p> In this paper, semi-orthogonal B-spline scaling functions and wavelets and their dual functions are presented to approximate the solutions of integro-differential equations.The B-spline scaling functions and wavelets, their properties and the operational matrices of derivative for this function are presented to reduce the solution of integro-differential equations to the solution of algebraic equations. Here we compute B-spline scaling functions of degree 4 and their dual, then we will show that by using them we have better approximation results for the solution of integro-differential equations in comparison with less degrees of scaling functions. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=%C4%B1ntegro-differential%20equations" title="ıntegro-differential equations">ıntegro-differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=quartic%20B-spline%20wavelet" title=" quartic B-spline wavelet"> quartic B-spline wavelet</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=dual%20functions" title=" dual functions"> dual functions</a> </p> <a href="https://publications.waset.org/abstracts/5002/numerical-solution-for-integro-differential-equations-by-using-quartic-b-spline-wavelet-and-operational-matrices" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/5002.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">456</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">4119</span> Numerical Treatment of Block Method for the Solution of Ordinary Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=A.%20M.%20Sagir">A. M. Sagir</a> </p> <p class="card-text"><strong>Abstract:</strong></p> Discrete linear multistep block method of uniform order for the solution of first order Initial Value Problems (IVPs) in Ordinary Differential Equations (ODEs) is presented in this paper. The approach of interpolation and collocation approximation are adopted in the derivation of the method which is then applied to first order ordinary differential equations with associated initial conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain four discrete schemes, which were used in block form for parallel or sequential solutions of the problems. Furthermore, a stability analysis and efficiency of the block method are tested on ordinary differential equations, and the results obtained compared favorably with the exact solution. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=block%20method" title="block method">block method</a>, <a href="https://publications.waset.org/abstracts/search?q=first%20order%20ordinary%20differential%20equations" title=" first order ordinary differential equations"> first order ordinary differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid" title=" hybrid"> hybrid</a>, <a href="https://publications.waset.org/abstracts/search?q=self-starting" title=" self-starting "> self-starting </a> </p> <a href="https://publications.waset.org/abstracts/3426/numerical-treatment-of-block-method-for-the-solution-of-ordinary-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/3426.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">482</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">4118</span> Integral Image-Based Differential Filters</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Kohei%20Inoue">Kohei Inoue</a>, <a href="https://publications.waset.org/abstracts/search?q=Kenji%20Hara"> Kenji Hara</a>, <a href="https://publications.waset.org/abstracts/search?q=Kiichi%20Urahama"> Kiichi Urahama</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We describe a relationship between integral images and differential images. First, we derive a simple difference filter from conventional integral image. In the derivation, we show that an integral image and the corresponding differential image are related to each other by simultaneous linear equations, where the numbers of unknowns and equations are the same, and therefore, we can execute the integration and differentiation by solving the simultaneous equations. We applied the relationship to an image fusion problem, and experimentally verified the effectiveness of the proposed method. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=integral%20images" title="integral images">integral images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20images" title=" differential images"> differential images</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20filters" title=" differential filters"> differential filters</a>, <a href="https://publications.waset.org/abstracts/search?q=image%20fusion" title=" image fusion"> image fusion</a> </p> <a href="https://publications.waset.org/abstracts/8531/integral-image-based-differential-filters" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/8531.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">506</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">4117</span> Stability of Hybrid Stochastic Systems</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Manlika%20Ratchagit">Manlika Ratchagit</a> </p> <p class="card-text"><strong>Abstract:</strong></p> This paper is concerned with robust mean square stability of uncertain stochastic switched discrete time-delay systems. The system to be considered is subject to interval time-varying delays, which allows the delay to be a fast time-varying function and the lower bound is not restricted to zero. Based on the discrete Lyapunov functional, a switching rule for the robust mean square stability for the uncertain stochastic discrete time-delay system is designed via linear matrix inequalities. Finally, some examples are exploited to illustrate the effectiveness of the proposed schemes. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=robust%20mean%20square%20stability" title="robust mean square stability">robust mean square stability</a>, <a href="https://publications.waset.org/abstracts/search?q=discrete-time%20stochastic%20systems" title=" discrete-time stochastic systems"> discrete-time stochastic systems</a>, <a href="https://publications.waset.org/abstracts/search?q=hybrid%20systems" title=" hybrid systems"> hybrid systems</a>, <a href="https://publications.waset.org/abstracts/search?q=interval%20time-varying%20delays" title=" interval time-varying delays"> interval time-varying delays</a>, <a href="https://publications.waset.org/abstracts/search?q=Lyapunov%20functional" title=" Lyapunov functional"> Lyapunov functional</a>, <a href="https://publications.waset.org/abstracts/search?q=linear%20matrix%20inequalities" title=" linear matrix inequalities"> linear matrix inequalities</a> </p> <a href="https://publications.waset.org/abstracts/20283/stability-of-hybrid-stochastic-systems" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/20283.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">485</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">4116</span> Series Solutions to Boundary Value Differential Equations</h5> <div class="card-body"> <p class="card-text"><strong>Authors:</strong> <a href="https://publications.waset.org/abstracts/search?q=Armin%20Ardekani">Armin Ardekani</a>, <a href="https://publications.waset.org/abstracts/search?q=Mohammad%20Akbari"> Mohammad Akbari</a> </p> <p class="card-text"><strong>Abstract:</strong></p> We present a method of generating series solutions to large classes of nonlinear differential equations. The method is well suited to be adapted in mathematical software and unlike the available commercial solvers, we are capable of generating solutions to boundary value ODEs and PDEs. Many of the generated solutions converge to closed form solutions. Our method can also be applied to systems of ODEs or PDEs, providing all the solutions efficiently. As examples, we present results to many difficult differential equations in engineering fields. <p class="card-text"><strong>Keywords:</strong> <a href="https://publications.waset.org/abstracts/search?q=computational%20mathematics" title="computational mathematics">computational mathematics</a>, <a href="https://publications.waset.org/abstracts/search?q=differential%20equations" title=" differential equations"> differential equations</a>, <a href="https://publications.waset.org/abstracts/search?q=engineering" title=" engineering"> engineering</a>, <a href="https://publications.waset.org/abstracts/search?q=series" title=" series"> series</a> </p> <a href="https://publications.waset.org/abstracts/54764/series-solutions-to-boundary-value-differential-equations" class="btn btn-primary btn-sm">Procedia</a> <a href="https://publications.waset.org/abstracts/54764.pdf" target="_blank" class="btn btn-primary btn-sm">PDF</a> <span class="bg-info text-light px-1 py-1 float-right rounded"> 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