A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations
type: Item
instance of: scholarly article
title: A product integration approach based on new orthogonal polynomials for nonlinear weakly singular integral equations
zbMATH Open document ID: 1192.65165
author: B. E. Eshmatov
published in: Acta Applicandae Mathematicae
publication date: 2010-05-26T00:00:00Z
review text: The authors investigate an approach of the product integration algorithm for the numerical solution of nonlinear Volterra integral equations of the second kind for a class, based on the paper of \textit{V. S. Chelyshkov} [ETNA, Electron. Trans. Numer. Anal. 25, 17--26, electronic only (2006; Zbl 1107.33006)], using the Lagrange interpolating polynomial.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45G05
Mathematics Subject Classification ID: 45D05
zbMATH DE Number: 5712196
zbMATH Keywords: nonlinear weakly singular integral equation
zbMATH Keywords: product integration
zbMATH Keywords: orthogonal polynomials
zbMATH Keywords: convergence
zbMATH Keywords: nonlinear Volterra integral equations of the second kind
reviewed by: Chuangan Hu
MaRDI profile type: Publication
full work available at URL: s10440-008-9351-y
OpenAlex ID: W2150591536
cites work: An Existence Theorem for Abel Integral Equations
cites work: A new approach to the numerical solution of weakly singular Volterra integral equations.
cites work: The Numerical Solution of Weakly Singular Volterra Integral Equations by Collocation on Graded Meshes
cites work: Q3750978
cites work: The piecewise polynomial collocation method for nonlinear weakly singular Volterra equations
cites work: Alternative orthogonal polynomials and quadratures
cites work: Convergence Properties of a Class of Product Formulas for Weakly Singular Integral Equations
cites work: Gauss-Type Quadratures for Weakly Singular Integrals and their Application to Fredholm Integral Equations of the Second Kind
cites work: Solving integral equations with logarithmic kernels by Chebyshev polynomials
cites work: Temperature of a nonlinearly radiating semi-infinite solid
cites work: Q3847247
cites work: Q4791731
cites work: A nonlinear Volterra equation arising in the theory of superfluidity
cites work: Q3681889
cites work: High order methods for weakly singular integral equations with nonsmooth input functions
cites work: A Further Extension of the Euler-Maclaurin Summation Formula
cites work: Orthogonal polynomials
cites work: Mean Convergence of Lagrange Interpolation. III
cites work: Product integration for Volterra integral equations of the second kind with weakly singular kernels
cites work: Application of Jacobi Polynomials to the Approximate Solution of a Singular Integral Equation with Cauchy Kernel on the Real Half-line
cites work: A generalization of discrete Gronwall inequality and its application to weakly singular Volterra integral equation of the second kind
cites work: Extrapolation method for solving weakly singular nonlinear Volterra integral equations of the second kind
cites work: A reliable technique for solving the weakly singular second-kind Volterra-type integral equations
DOI: 10.1007/S10440-008-9351-Y
description: scientific article; zbMATH DE number 5712196