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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)
Abstract
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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*Corresponding author. Email addresses: cjzhang@mail.hust.edu.cn (C. Zhang), wenjieshihust@gmail.com (W. Shi)
References
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East Asian Journal on Applied Mathematics
  • ISSN: 2079-7362
  • EISSN: 2079-7370
  • URL: /core/journals/east-asian-journal-on-applied-mathematics
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