On the wavelet Galerkin method for solving the fractional Fredholm integro-differential equations

Articles in Press

Document Type : Research Paper

Authors

1 Department of Mathematics, Tabriz Branch, Islamic Azad University, Tabriz, Iran.

2 Department of Mathematics, Institute for Advanced Studies in Basic Sciences (IASBS), Zanjan 45137-66731, Iran.

Abstract

An effective scheme is presented to estimate the numerical solution of fractional integro-differential equations (FIDEs). In the present method, to obtain the solution of the FIDEs, they must be first reduced to the corresponding Volterra-Fredholm integral equations (VFIEs) with the weakly singular kernel. Then, applying the matrix that represents the fractional integral (FI) based on biorthogonal Hermite cubic spline scaling bases (BHCSSb), and using the wavelet Galerkin method, the reduced problem can be solved. The combination of singularity and the challenge related to nonlinearity poses a formidable obstacle in solving the desired equations, but our method overcomes them well. Our investigation of the method convergence is provided, and it verifies that the convergence rate is $O(2^{-J})$ where $J\in \mathbb{N}_0$ is the refinement level. Convergence verification has also been done by presenting several numerical examples. Compared to other methods, it has been shown that the obtained results have better accuracy.

Keywords

Main Subjects

Computational Methods for Differential Equations

Articles in Press, Accepted Manuscript
Available Online from 07 October 2024

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History

  • Receive Date: 20 June 2024
  • Revise Date: 21 August 2024
  • Accept Date: 06 October 2024

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