Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

Year:    2018

Author:    Xingfa Yang, Yin Yang, Yanping Chen, Jie Liu

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1440–1458

Abstract

In this paper, we study a class of nonlinear fractional integro-differential equations. The fractional derivative is described in the Caputo sense. Using the properties of the Caputo derivative, we convert the fractional integro-differential equations into equivalent integral-differential equations of Volterra type with singular kernel, then we propose and analyze a spectral Jacobi-collocation approximation for nonlinear integro-differential equations of Volterra type. We provide a rigorous error analysis for the spectral methods, which shows that both the errors of approximate solutions and the errors of approximate fractional derivatives of the solutions decay exponentially in $L^∞$-norm and weighted $L^2$-norm.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2018-0038

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 6 : pp. 1440–1458

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    19

Keywords:    Spectral method nonlinear fractional derivative Volterra integro-differential equations Caputo derivative.

Author Details

Xingfa Yang

Yin Yang

Yanping Chen

Jie Liu