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A numerical method based on three-dimensional Legendre wavelet method for two-dimensional time-fractional diffusion equation. (English) Zbl 1505.65272

Summary: 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.

MSC:

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
65T60 Numerical methods for wavelets
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs

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