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Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels

Generalized Jacobi Spectral-Galerkin Method for Nonlinear Volterra Integral Equations with Weakly Singular Kernels
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Year:    2015

Author:    Jie Shen, Changtao Sheng, Zhongqing Wang

Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 315–329

Abstract

We propose a generalized Jacobi spectral-Galerkin method for the nonlinear Volterra integral equations (VIEs) with weakly singular kernels. We establish the existence and uniqueness of the numerical solution, and characterize the convergence of the proposed method under reasonable assumptions on the nonlinearity. We also present numerical results which are consistent with the theoretical predictions.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jms.v48n4.15.01

Journal of Mathematical Study, Vol. 48 (2015), Iss. 4 : pp. 315–329

Published online:    2015-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    15

Keywords:    Generalized Jacobi spectral-Galerkin method nonlinear Volterra integral equations with weakly singular kernels convergence analysis.

Author Details

Jie Shen

Changtao Sheng

Zhongqing Wang

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