A new wavelet method for solving a class of nonlinear Volterra-Fredholm integral equations
type: Item
instance of: scholarly article
title: A new wavelet method for solving a class of nonlinear Volterra-Fredholm integral equations
zbMATH Open document ID: 1474.65519
DOI: 10.1155/2014/975985
published in: Abstract and Applied Analysis
publication date: 2019-02-14T00:00:00Z
review text: Summary: A new approach, Coiflet-type wavelet Galerkin method, is proposed for numerically solving the Volterra-Fredholm integral equations. Based on the Coiflet-type wavelet approximation scheme, arbitrary nonlinear term of the unknown function in an equation can be explicitly expressed. By incorporating such a modified wavelet approximation scheme into the conventional Galerkin method, the nonsingular property of the connection coefficients significantly reduces the computational complexity and achieves high precision in a very simple way. Thus, one can obtain a stable, highly accurate, and efficient numerical method without calculating the connection coefficients in traditional Galerkin method for solving the nonlinear algebraic equations. At last, numerical simulations are performed to show the efficiency of the method proposed.
Mathematics Subject Classification ID: 65R20
Mathematics Subject Classification ID: 45B05
Mathematics Subject Classification ID: 45D05
Mathematics Subject Classification ID: 65T60
zbMATH DE Number: 7023437
author: Xiaomin Wang
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1155/2014/975985
OpenAlex ID: W2056525254
Wikidata QID: Q59043251
cites work: Asymptotic bounds for solutions to a system of damped integrodifferential equations of electromagnetic theory
cites work: Fredholm-Volterra integral equation of the first kind and contact problem
cites work: A Galerkin solution to a regularized Cauchy singular integro-differential equation
cites work: Taylor collocation method and convergence analysis for the Volterra-Fredholm integral equations
cites work: On mixed collocation methods for Volterra integral equations with periodic solution
cites work: A method for the approximate solution of the second‐order linear differential equations in terms of Taylor polynomials
cites work: A Taylor Collocation Method for the Solution of Linear Integro-Differential Equations
cites work: A Taylor collocation method for the approximate solution of general linear Fredholm-Volterra integro-difference equations with mixed argument
cites work: A numerical method for solving a class of functional and two-dimensional integral equations
cites work: Numerical solution of nonlinear Fredholm integral equations of the second kind using Haar wavelets
cites work: Solving second kind integral equations by Galerkin methods with continuous orthogonal wavelets
cites work: The Coiflet-Galerkin method for linear Volterra integral equations
cites work: A simple Taylor-series expansion method for a class of second kind integral equations
cites work: Lagrange interpolation to compute the numerical solutions of differential, integral and integro-differential equations
cites work: Lagrange collocation method for solving Volterra-Fredholm integral equations
cites work: Spectral methods for weakly singular Volterra integral equations with smooth solutions
cites work: Exact solutions of multi-term fractional diffusion-wave equations with Robin type boundary conditions
cites work: A Wavelet Numerical Method for Solving Nonlinear Fractional Vibration, Diffusion and Wave Equations
cites work: Wavelet-Galerkin method for integro-differential equations
cites work: Q4937609
cites work: Computation of the Laplace inverse transform by application of the wavelet theory
cites work: A wavelet approach for active-passive vibration control of laminated plates
cites work: Numerical solution of functional differential, integral and integro-differential equations
cites work: Wavelet Galerkin method for numerical solution of nonlinear integral equation
description: scientific article; zbMATH DE number 7023437