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Volume 8, Issue 4
Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations

Sun Tao, Rui-Qing Liu & Li-Lian Wang

DOI: 10.4208/eajam.050818.071018

East Asian J. Appl. Math., 8 (2018), pp. 611-633.

Published online: 2018-10

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  • 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.

  • Keywords

Mapped Jacobi polynomials, generalised Müntz-Jacobi functions, singularly perturbed fractional differential equations, Petrov-Galerkin methods.

  • AMS Subject Headings

65N35, 65E05, 65L11, 26A33, 34A08, 34K26, 41A10

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{EAJAM-8-611, author = {Tao , SunLiu , Rui-Qing and Wang , Li-Lian}, title = {Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations}, journal = {East Asian Journal on Applied Mathematics}, year = {2018}, volume = {8}, number = {4}, pages = {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.

}, issn = {2079-7370}, doi = {https://doi.org/10.4208/eajam.050818.071018}, url = {http://global-sci.org/intro/article_detail/eajam/12811.html} }
TY - JOUR T1 - Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations AU - Tao , Sun AU - Liu , Rui-Qing AU - Wang , Li-Lian JO - East Asian Journal on Applied Mathematics VL - 4 SP - 611 EP - 633 PY - 2018 DA - 2018/10 SN - 8 DO - http://doi.org/10.4208/eajam.050818.071018 UR - https://global-sci.org/intro/article_detail/eajam/12811.html KW - Mapped Jacobi polynomials, generalised Müntz-Jacobi functions, singularly perturbed fractional differential equations, Petrov-Galerkin methods. AB -

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.

Tao , SunLiu , Rui-Qing and Wang , Li-Lian. (2018). Generalised Müntz Spectral Galerkin Methods for Singularly Perturbed Fractional Differential Equations. East Asian Journal on Applied Mathematics. 8 (4). 611-633. doi:10.4208/eajam.050818.071018
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