Shifted Legendre Tau Method for Solving the Stochastic Weakly Singular Integro-Differential Equations

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 Science, Damghan University, Damghan, Iran

Abstract

‎In this paper‎, ‎the stochastic weakly singular integro-differential equation is discussed‎. ‎The shifted Legendre Tau method is introduced for finding the unknown function‎. ‎For this purpose‎, ‎shifted Legendre polynomials and their properties are introduced‎. ‎The proposed method is based on expanding the approximate solution as the elements of shifted Legendre polynomials‎. ‎We reduce the problem to set of algebraic equations by using operational matrices‎. ‎Also the convergence analysis of shifted Legendre polynomials and error estimation for this method have been discussed‎. ‎Finally‎, ‎several numerical examples are given to demonstrate the high accuracy of the method‎.

Keywords

References

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Global Analysis and Discrete Mathematics
Volume 6, Issue 2
November 2021
Pages 269-291

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History

  • Receive Date: 13 January 2022
  • Revise Date: 17 February 2022
  • Accept Date: 23 February 2022

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