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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.
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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