CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS

doi:10.1016/S0252-9602(14)60039-4

Abstract

Abstract:

We propose and analyze a spectral Jacobi-collocation approximation for frac-tional order integro-differential equations of Volterra type. The fractional derivative is de-scribed in the Caputo sense. We provide a rigorous error analysis for the collection method, which shows that the errors of the approximate solution decay exponentially in L^∞ norm and weighted L²-norm. The numerical examples are given to illustrate the theoretical results.

Key words: Spectral Jacobi-collocation method, fractional order integro-differential equa-tions, Caputo derivative

CLC Number:

65R20

YANG Yin, CHEN Yan-Ping, HUANG Yun-Qing. CONVERGENCE ANALYSIS OF THE JACOBI SPECTRAL-COLLOCATION METHOD FOR FRACTIONAL INTEGRO-DIFFERENTIAL EQUATIONS[J].Acta mathematica scientia,Series B, 2014, 34(3): 673-690.

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