Legendre Spectral Tau Method for Solving the Fractional Integro-Differential Equations with A Weakly Singular Kernel

Document Type : Research Paper

Authors

1 Associate Professor, Mathematics and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran

2 Associate Professor,Mathematica and Computer Science Department, Adib mazandaran institute of higher education, Sari, Iran

3 School of Mathematics and Computer Sciences, Damghan University, P.O.Box 36715-364, Damghan, Iran.

Abstract

‎In this paper‎, ‎the Tau method based on shifted Legendre polynomials has been introduced to approximate the numerical solutions of a class of fractional integro-differential equations with a weakly singular kernel‎ . ‎By using operational matrices we reduce the problem to a set of algebraic equations‎ . ‎Also the upper bound of the error of the shifted Legendre expansion is investigated‎. ‎Finally‎, ‎several numerical examples are given to illustrate the high accuracy of the method‎.

Keywords

References

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Global Analysis and Discrete Mathematics
Volume 7, Issue 1
November 2022
Pages 11-31

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History

  • Receive Date: 12 January 2022
  • Revise Date: 13 February 2022
  • Accept Date: 23 February 2022

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