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Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations

Author

Listed:
  • Yanmei Liu

    (Department of Mathematics, LuLiang University, Lishi 033000, China
    These authors contributed equally to this work.)

  • Monzorul Khan

    (Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
    These authors contributed equally to this work.)

  • Yubin Yan

    (Department of Mathematics, University of Chester, Chester CH1 4BJ, UK
    These authors contributed equally to this work.)

Abstract

Fourier spectral methods for solving some linear stochastic space-fractional partial differential equations perturbed by space-time white noises in the one-dimensional case are introduced and analysed. The space-fractional derivative is defined by using the eigenvalues and eigenfunctions of the Laplacian subject to some boundary conditions. We approximate the space-time white noise by using piecewise constant functions and obtain the approximated stochastic space-fractional partial differential equations. The approximated stochastic space-fractional partial differential equations are then solved by using Fourier spectral methods. Error estimates in the L 2 -norm are obtained, and numerical examples are given.

Suggested Citation

  • Yanmei Liu & Monzorul Khan & Yubin Yan, 2016. "Fourier Spectral Methods for Some Linear Stochastic Space-Fractional Partial Differential Equations," Mathematics, MDPI, vol. 4(3), pages 1-28, July.
    • Handle: RePEc:gam:jmathe:v:4:y:2016:i:3:p:45-:d:73231
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    References listed on IDEAS

    as
    1. Röckner, Michael & Zhu, Rongchan & Zhu, Xiangchan, 2014. "Local existence and non-explosion of solutions for stochastic fractional partial differential equations driven by multiplicative noise," Stochastic Processes and their Applications, Elsevier, vol. 124(5), pages 1974-2002.
    2. Debbi, Latifa & Dozzi, Marco, 2005. "On the solutions of nonlinear stochastic fractional partial differential equations in one spatial dimension," Stochastic Processes and their Applications, Elsevier, vol. 115(11), pages 1764-1781, November.
    Full references (including those not matched with items on IDEAS)

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