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

Authors

  • Jie Shen School of Mathematical Science, Xiamen University, Xiamen 361005, P. R. China
  • Changtao Sheng School of Mathematical Sciences and Fujian Provincial Key Laboratory on Mathematical Modeling & High Performance Scientific Computing, Xiamen University, Xiamen 361005, Fujian, P. R. China
  • Zhongqing Wang School of Science, University of Shanghai for Science and Technology, Shanghai 200093, P. R. China

DOI:

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

Keywords:

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

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.

Downloads

Published

2021-11-08

Issue

Vol. 48 No. 4 (2015)

Section

Articles