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Saadatmandi, Abbas; Dehghan, Mehdi

A tau approach for solution of the space fractional diffusion equation. (English) Zbl 1228.65203

Comput. Math. Appl. 62, No. 3, 1135-1142 (2011).
Summary: Fractional differentials provide more accurate models of systems under consideration. In this paper, approximation techniques based on the shifted Legendre-tau idea are presented to solve a class of initial-boundary value problems for the fractional diffusion equations with variable coefficients on a finite domain. The fractional derivatives are described in the Caputo sense. The technique is derived by expanding the required approximate solution as the elements of shifted Legendre polynomials. Using the operational matrix of the fractional derivative the problem can be reduced to a set of linear algebraic equations. From the computational point of view, the solution obtained by this method is in excellent agreement with those obtained by previous work in the literature and also it is efficient to use.

Cited in 1 Review
Cited in 101 Documents

MSC:

65M99 Numerical methods for partial differential equations, initial value and time-dependent initial-boundary value problems
35R11 Fractional partial differential equations

Keywords:

fractional diffusion equation; operational matrix; Legendre polynomials; tau method; Caputo derivative
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\textit{A. Saadatmandi} and \textit{M. Dehghan}, Comput. Math. Appl. 62, No. 3, 1135--1142 (2011; Zbl 1228.65203)
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