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

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

Published online: 2018-09

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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 $L^2$-norm.

65R20, 45J05, 65N12

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@Article{AAMM-10-1440, author = {Yang , XingfaYang , YinChen , Yanping and Liu , Jie}, title = {Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {6}, pages = {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.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2018-0038}, url = {http://global-sci.org/intro/article_detail/aamm/12718.html} }
TY - JOUR T1 - Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations AU - Yang , Xingfa AU - Yang , Yin AU - Chen , Yanping AU - Liu , Jie JO - Advances in Applied Mathematics and Mechanics VL - 6 SP - 1440 EP - 1458 PY - 2018 DA - 2018/09 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2018-0038 UR - https://global-sci.org/intro/article_detail/aamm/12718.html KW - Spectral method, nonlinear, fractional derivative, Volterra integro-differential equations, Caputo derivative. AB -

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.

Xingfa Yang, Yin Yang, Yanping Chen & Jie Liu. (1970). Jacobi Spectral Collocation Method Based on Lagrange Interpolation Polynomials for Solving Nonlinear Fractional Integro-Differential Equations. Advances in Applied Mathematics and Mechanics. 10 (6). 1440-1458. doi:10.4208/aamm.OA-2018-0038
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