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

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

Year:    2017

East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/eajam.150616.071216a

East Asian Journal on Applied Mathematics, Vol. 7 (2017), Iss. 2 : pp. 306–324

Published online:    2017-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Random differential equations piecewise constant argument generalised polynomial chaos finite-dimensional noise error analysis.