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The sinc-Legendre collocation method for a class of fractional convection-diffusion equations with variable coefficients. (English) Zbl 1250.65121
Summary: This paper deals with the numerical solution of classes of fractional convection-diffusion equations with variable coefficients. The fractional derivatives are described based on the Caputo sense. Our approach is based on the collocation techniques. The method consists of reducing the problem to the solution of linear algebraic equations by expanding the required approximate solution as the elements of shifted Legendre polynomials in time and the sinc functions in space with unknown coefficients. The properties of sinc functions and shifted Legendre polynomials are then utilized to evaluate the unknown coefficients. Several examples are given and the numerical results are shown to demonstrate the efficiency of the newly proposed method.

65M70 Spectral, collocation and related methods for initial value and initial-boundary value problems involving PDEs
35K05 Heat equation
35R11 Fractional partial differential equations
Full Text: DOI
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