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Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument

Part of: Numerical analysis: Ordinary differential equations Probabilistic methods, simulation and stochastic differential equations

Published online by Cambridge University Press:  02 May 2017

Chengjian Zhang  and
Wenjie Shi
Chengjian Zhang*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China
Wenjie Shi*
Affiliation:
School of Mathematics and Statistics, Huazhong University of Science and Technology, Wuhan 430074, China School of Mathematics and Computer Science, Wuhan Textile University, Wuhan 430073, China
*
*Corresponding author. Email addresses:cjzhang@mail.hust.edu.cn (C. Zhang), wenjieshihust@gmail.com (W. Shi)
*Corresponding author. Email addresses:cjzhang@mail.hust.edu.cn (C. Zhang), wenjieshihust@gmail.com (W. Shi)
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Abstract

We propose a class of numerical methods for solving nonlinear random differential equations with piecewise constant argument, called gPCRK methods as they combine generalised polynomial chaos with Runge-Kutta methods. An error analysis is presented involving the error arising from a finite-dimensional noise assumption, the projection error, the aliasing error and the discretisation error. A numerical example is given to illustrate the effectiveness of this approach.

Keywords

Random differential equationspiecewise constant argumentgeneralised polynomial chaosfinite-dimensional noiseerror analysis

MSC classification

Secondary: 65L70: Error bounds 65C30: Stochastic differential and integral equations
Type
Research Article
Information
East Asian Journal on Applied Mathematics , Volume 7 , Issue 2 , May 2017 , pp. 306 - 324
Copyright
Copyright © Global-Science Press 2017 

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