The L2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations

Authors:
Payam Mokhtary;Farideh Ghoreishi
Affiliations:
Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran;Department of Mathematics, K. N. Toosi University of Technology, Tehran, Iran
Venue:
Numerical Algorithms
Year:
2011

Citing 4
Cited 1

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)

Theory and Applications of Fractional Differential Equations, Volume 204 (North-Holland Mathematics Studies)
An efficient method for solving systems of fractional integro-differential equations

Computers & Mathematics with Applications
The adaptive operational Tau method for systems of ODEs

Journal of Computational and Applied Mathematics
An extension of the spectral Tau method for numerical solution of multi-order fractional differential equations with convergence analysis

Computers & Mathematics with Applications

Application of the collocation method for solving nonlinear fractional integro-differential equations

Journal of Computational and Applied Mathematics

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Abstract

The operational Tau method, a well known method for solving functional equations is employed to approximate the solution of nonlinear fractional integro-differential equations. The fractional derivatives are described in the Caputo sense. The unique solvability of the linear Tau algebraic system is discussed. In addition, we provide a rigorous convergence analysis for the Legendre Tau method which indicate that the proposed method converges exponentially provided that the data in the given FIDE are smooth. To do so, Sobolev inequality with some properties of Banach algebras are considered. Some numerical results are given to clarify the efficiency of the method.