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Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension

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  • Zheng, Xiangcheng
  • Ervin, V.J.
  • Wang, Hong

Abstract

In this article we consider the approximation of a variable coefficient (two-sided) fractional diffusion equation (FDE), having unknown u. By introducing an intermediate unknown, q, the variable coefficient FDE is rewritten as a lower order, constant coefficient FDE. A spectral approximation scheme, using Jacobi polynomials, is presented for the approximation of q, qN. The approximate solution to u, uN, is obtained by post processing qN. An a priori error analysis is given for (q−qN) and (u−uN). Two numerical experiments are presented whose results demonstrate the sharpness of the derived error estimates.

Suggested Citation

  • Zheng, Xiangcheng & Ervin, V.J. & Wang, Hong, 2019. "Spectral approximation of a variable coefficient fractional diffusion equation in one space dimension," Applied Mathematics and Computation, Elsevier, vol. 361(C), pages 98-111.
    • Handle: RePEc:eee:apmaco:v:361:y:2019:i:c:p:98-111
    DOI: 10.1016/j.amc.2019.05.017
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    Cited by:

    1. Zhang, Xue & Gu, Xian-Ming & Zhao, Yong-Liang & Li, Hu & Gu, Chuan-Yun, 2024. "Two fast and unconditionally stable finite difference methods for Riesz fractional diffusion equations with variable coefficients," Applied Mathematics and Computation, Elsevier, vol. 462(C).

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