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

Chengjian Zhang & Wenjie Shi

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 = {}, 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 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 & Wenjie Shi. (2020). 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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