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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:
65L05Initial value problems for ODE (numerical methods)
34A08Fractional differential equations
34A34Nonlinear ODE and systems, general
65L60Finite elements, Rayleigh-Ritz, Galerkin and collocation methods for ODE
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