Tau approximate solution of fractional partial differential equations

Authors:
S. Karimi Vanani;A. Aminataei
Affiliations:
-;-
Venue:
Computers & Mathematics with Applications
Year:
2011

Citing 6
Cited 1

Tau method approximation of differential eigenvalue problems where the spectral parameter enters nonlinearly

Journal of Computational Physics
Numerical solution of ordinary and partial functional-differential eigenvalue problems with the Tau method

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Iterated solutions of linear operator equations with the Tau method

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An explicit and numerical solutions of the fractional KdV equation

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Comparison between the homotopy perturbation method and the variational iteration method for linear fractional partial differential equations

Computers & Mathematics with Applications
A novel method for nonlinear fractional partial differential equations: Combination of DTM and generalized Taylor's formula

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A Chebyshev spectral method based on operational matrix for initial and boundary value problems of fractional order

Computers & Mathematics with Applications

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Abstract

In this study, we improve the algebraic formulation of the fractional partial differential equations (FPDEs) by using the matrix-vector multiplication representation of the problem. This representation allows us to investigate an operational approach of the Tau method for the numerical solution of FPDEs. We introduce a converter matrix for the construction of converted Chebyshev and Legendre polynomials which is applied in the operational approach of the Tau method. We present the advantages of using the method and compare it with several other methods. Some experiments are applied to solve FPDEs including linear and nonlinear terms. By comparing the numerical results obtained from the other methods, we demonstrate the high accuracy and efficiency of the proposed method.