Research PaperNo Access

A numerical method based on three-dimensional Legendre wavelet method for two-dimensional time-fractional diffusion equation

Sarkout Abdi

Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, P.O. Box 41335-3516, P.C. 4147654919, Iran

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Aram Azizi

Department of Mathematics, Payame Noor University, P.O. Box 19395-3697 Tehran, Iran

E-mail Address: a.azizi@pnu.ac.ir

Corresponding author.

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Mahmoud Shafiee

Department of Mathematics, Rasht Branch, Islamic Azad University, Rasht, P.O. Box 41335-3516, P.C. 4147654919, Iran

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, and

Jamshid Saeidian

https://orcid.org/0000-0003-3991-1701

Faculty of Mathematical Sciences and Computer, Kharazmi University, 50 Taleghani avenue, Tehran 1561836314, Iran

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https://doi.org/10.1142/S0219691321500089Cited by:1 (Source: Crossref)

Abstract

In this paper, an efficient numerical method is proposed to handle two-dimensional fractional diffusion equations on a finite domain. The proposed method combines the product of Legendre wavelet bases for two spatial dimensions and a time direction. The operational matrix of the proposed method is obtained. Tikhonov regularization is employed to stabilize the system in cases where the final linear system of equations is large. The convergence analysis of the method is studied and some numerical examples are presented to investigate the efficiency and accuracy of the method.

Keywords:

AMSC: 26A33, 46F12, 80M25

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