Numerical solution of space-time fractional PDEs using RBF-QR and Chebyshev polynomials

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In this study, we propose a numerical discretization of space-time fractional partial differential equations (PDEs) with variable coefficients, based on the radial basis functions (RBF) and pseudospectral (PS) methods. The RBF method is used for space discretization, while Chebyshev polynomials handle time discretization. The use of PS methods significantly reduces the number of nodes needed to obtain the solution. The proposed numerical scheme is capable of handling all three types of boundary conditions: Dirichlet, Neumann and Robin. We give numerical examples to validate our method and to show its superior performance compared to other techniques.

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© 2019 IMACS. Published by Elsevier B.V. All rights reserved. Publisher's version of record: https://doi.org/10.1016/j.apnum.2019.04.012

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Applied Numerical Mathematics