The L2-convergence of the Legendre spectral Tau matrix formulation for nonlinear fractional integro differential equations
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- Mokhtary, P. & Ghoreishi, F. Numer Algor (2011) 58: 475. doi:10.1007/s11075-011-9465-6
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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.