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A pseudo-spectral scheme for the approximate solution of a family of fractional differential equations. (English) Zbl 1226.65062
Author’s abstract: The pseudo-spectral method is generalized for solving fractional differential equations with initial conditions. For this purpose, an appropriate representation of the solution is presented and the pseudo-spectral differentiation matrix of fractional order is derived. Then, by using a pseudo-spectral scheme, the problem is reduced to the solution of a system of algebraic equations. Through several numerical examples we evaluate the accuracy and performance of our proposed method.

MSC:
65L05 Numerical methods for initial value problems
34A08 Fractional ordinary differential equations and fractional differential inclusions
34A34 Nonlinear ordinary differential equations and systems, general theory
65L60 Finite element, Rayleigh-Ritz, Galerkin and collocation methods for ordinary differential equations
Software:
ma2dfc; Matlab; OPQ
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References:
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