Convergence analysis of generalized Jacobi-Galerkin methods for second kind Volterra integral equations with weakly singular kernels
type: Item
instance of: scholarly article
title: Convergence analysis of generalized Jacobi-Galerkin methods for second kind Volterra integral equations with weakly singular kernels
zbMATH Open document ID: 1376.65153
DOI: 10.1155/2017/4751357
author: Haotao Cai
published in: Journal of Function Spaces
publication date: 2017-11-01T00:00:00Z
review text: Summary: We develop a generalized Jacobi-Galerkin method for second kind Volterra integral equations with weakly singular kernels. In this method, we first introduce some known singular nonpolynomial functions in the approximation space of the conventional Jacobi-Galerkin method. Secondly, we use the Gauss-Jacobi quadrature rules to approximate the integral term in the resulting equation so as to obtain high-order accuracy for the approximation. Then, we establish that the approximate equation has a unique solution and the approximate solution arrives at an optimal convergence order. One numerical example is presented to demonstrate the effectiveness of the proposed method.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 45E10
zbMATH DE Number: 6802003
zbMATH Keywords: Jacobi-Galerkin method
zbMATH Keywords: second kind Volterra integral equations
zbMATH Keywords: weakly singular kernels
zbMATH Keywords: Gauss-Jacobi quadrature rules
zbMATH Keywords: convergence
zbMATH Keywords: numerical example
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2017/4751357
OpenAlex ID: W2752421330
cites work: The Numerical Solution of Integral Equations of the Second Kind
cites work: Collocation Methods for Volterra Integral and Related Functional Differential Equations
cites work: Nonpolynomial Spline Collocation for Volterra Equations with Weakly Singular Kernels
cites work: Analysis of collocation solutions for a class of functional equations with vanishing delays
cites work: Hybrid collocation methods for Fredholm integral equations with weakly singular kernels
cites work: A Hybrid Collocation Method for Volterra Integral Equations with Weakly Singular Kernels
cites work: Singularity preserving Galerkin methods for weakly singular Fredholm integral equations
cites work: Q5683194
cites work: A Jacobi-collocation method for solving second kind Fredholm integral equations with weakly singular kernels
cites work: Spectral methods for weakly singular Volterra integral equations with smooth solutions
cites work: Convergence analysis of the Jacobi spectral-collocation methods for Volterra integral equations with a weakly singular kernel
cites work: Numerical solutions for weakly singular Volterra integral equations using Chebyshev and Legendre pseudo-spectral Galerkin methods
cites work: Q5319785
cites work: Spectral Petrov-Galerkin methods for the second kind Volterra type integro-differential equations
cites work: Legendre spectral collocation methods for pantograph Volterra delay-integro-differential equations
cites work: Convergence analysis of spectral Galerkin methods for Volterra type integral equations
cites work: Spectral methods for weakly singular Volterra integral equations with pantograph delays
cites work: Linear integral equations
cites work: Spectral Methods
description: scientific article; zbMATH DE number 6802003