Convergence analysis of tau scheme for the fractional reaction-diffusion equation
School of Mathematics, Iran University of Science and Technology, Narmak, 16846-13114, Tehran, Iran
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Accepted: 9 August 2018
Published online: 4 October 2018
In this paper, an efficient numerical scheme is presented in order to solve the time Caputo fractional reaction-diffusion equation. This method is based on the Legendre tau spectral method combined with the generalized shifted Legendre operational matrix, and our main purpose is to reduce the given equation to the solution of a system of algebraic equations. The greatest advantage of this approach is its spectral convergence, and our focus is to derive the error estimate and convergence analysis of this scheme for the fractional reaction-diffusion equation. In order to illustrate the validity and the efficiency of this scheme, five test examples are provided and also numerical results are compared with the results of existing schemes.
© Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature, 2018