Volume 10, Issue 6
Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations

Xingfa Yang ,  Yin Yang ,  Yanping Chen and Jie Liu

10.4208/aamm.OA-2018-0038

Adv. Appl. Math. Mech., 10 (2018), pp. 1440-1458.

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  • 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 L2-norm.

  • History

Published online: 2018-09

  • AMS Subject Headings

65R20, 45J05, 65N12

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