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

Xiangcheng Zheng, V.J. Ervin and Hong Wang

Applied Mathematics and Computation, 2019, vol. 361, issue C, 98-111

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.

Keywords: Fractional diffusion equation; Jacobi polynomials; Spectral method (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (1)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:361:y:2019:i:c:p:98-111

DOI: 10.1016/j.amc.2019.05.017

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