Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations
Year: 2018
Author: Sun Tao, Rui-Qing Liu, Li-Lian Wang
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 611–633
Abstract
A family of orthogonal generalised Müntz-Jacobi functions is introduced and used for solving singularly perturbed fractional differential equations. Such basis functions can provide much better approximation for boundary layers or endpoint singularities than usual polynomial bases. The fractional integrals and derivatives of generalised Müntz-Jacobi functions are accurately calculated. The corresponding Petrov-Galerkin and Galerkin methods are very efficient. Numerical examples demonstrate a significant improvement in the accuracy of the methods.
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Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/eajam.050818.071018
East Asian Journal on Applied Mathematics, Vol. 8 (2018), Iss. 4 : pp. 611–633
Published online: 2018-01
AMS Subject Headings:
Copyright: COPYRIGHT: © Global Science Press
Pages: 23
Keywords: Mapped Jacobi polynomials generalised Müntz-Jacobi functions singularly perturbed fractional differential equations Petrov-Galerkin methods.