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Volume 7, Issue 2
Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument

Chengjian Zhang & Wenjie Shi

DOI: 10.4208/eajam.150616.071216a

East Asian J. Appl. Math., 7 (2017), pp. 306-324.

Published online: 2018-02

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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 equations, piecewise constant argument, generalised polynomial chaos, finite-dimensional noise, error analysis.

  • AMS Subject Headings

65L70, 65C30

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-7-306, author = {Chengjian Zhang and Wenjie Shi}, title = {Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {7}, number = {2}, pages = {306--324}, 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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.150616.071216a}, url = {http://global-sci.org/intro/article_detail/eajam/10751.html} }
TY - JOUR T1 - Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument AU - Chengjian Zhang & Wenjie Shi JO - East Asian Journal on Applied Mathematics VL - 2 SP - 306 EP - 324 PY - 2018 DA - 2018/02 SN - 7 DO - http://doi.org/10.4208/eajam.150616.071216a UR - https://global-sci.org/intro/article_detail/eajam/10751.html KW - Random differential equations, piecewise constant argument, generalised polynomial chaos, finite-dimensional noise, error analysis. AB -

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.

Chengjian Zhang and Wenjie Shi. (2018). Application of gPCRK Methods to Nonlinear Random Differential Equations with Piecewise Constant Argument. East Asian Journal on Applied Mathematics. 7 (2). 306-324. doi:10.4208/eajam.150616.071216a
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