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A Numerical Comparison of Finite Difference and Finite Element Methods for a Stochastic Differential Equation with Polynomial Chaos

  • Ning Li (a1), Bo Meng (a1), Xinlong Feng (a1) and Dongwei Gui (a2)

Abstract

A numerical comparison of finite difference (FD) and finite element (FE) methods for a stochastic ordinary differential equation is made. The stochastic ordinary differential equation is turned into a set of ordinary differential equations by applying polynomial chaos, and the FD and FE methods are then implemented. The resulting numerical solutions are all non-negative. When orthogonal polynomials are used for either continuous or discrete processes, numerical experiments also show that the FE method is more accurate and efficient than the FD method.

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Corresponding author

*Corresponding author. Email addresses: future_lining@163.com (N. Li), future_bo@163.com (B. Meng), fxlmath@gmail.com (X. Feng), dongwei@ms.xjb.ac.cn (D. Gui)

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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