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

  • Chengjian Zhang (a1) and Wenjie Shi (a1) (a2)


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.


Corresponding author

*Corresponding author. Email addresses: (C. Zhang), (W. Shi)


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