Optimal Petrov-Galerkin spectral approximation method for the fractional diffusion, advection, reaction equation on a bounded interval
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Publication:2027923
DOI10.1007/S10915-020-01366-YzbMATH Open1465.65154arXiv2002.02330OpenAlexW3123578074MaRDI QIDQ2027923
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Publication date: 28 May 2021
Published in: (Search for Journal in Brave)
Abstract: In this paper we investigate the numerical approximation of the fractional diffusion, advection, reaction equation on a bounded interval. Recently the explicit form of the solution to this equation was obtained. Using the explicit form of the boundary behavior of the solution and Jacobi polynomials, a Petrov-Galerkin approximation scheme is proposed and analyzed. Numerical experiments are presented which support the theoretical results, and demonstrate the accuracy and optimal convergence of the approximation method.
Full work available at URL: https://arxiv.org/abs/2002.02330
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