scholarly journals A Numerical solution to the linear and nonlinear Fredholm integral equations using Legendre wavelet functions

PAMM ◽  
2007 ◽  
Vol 7 (1) ◽  
pp. 2020149-2020150 ◽  
Author(s):  
S. Rahbar
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Linear And Nonlinear

scholarly journals Numerical Methods for Solving Fredholm Integral Equations of Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-17 ◽  
Author(s):  
S. Saha Ray ◽  
P. K. Sahu
Keyword(s):  
Integral Equation ◽  
Numerical Methods ◽  
Integral Equations ◽  
Applied Mathematics ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Linear And Nonlinear ◽  
Interdisciplinary Effort

Integral equation has been one of the essential tools for various areas of applied mathematics. In this paper, we review different numerical methods for solving both linear and nonlinear Fredholm integral equations of second kind. The goal is to categorize the selected methods and assess their accuracy and efficiency. We discuss challenges faced by researchers in this field, and we emphasize the importance of interdisciplinary effort for advancing the study on numerical methods for solving integral equations.

scholarly journals Numerical Solution of Nonlinear Fredholm Integrodifferential Equations of Fractional Order by Using Hybrid Functions and the Collocation Method

2012 ◽  
Vol 2012 ◽  
pp. 1-11 ◽  
Author(s):  
Jianhua Hou ◽  
Beibo Qin ◽  
Changqing Yang
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Taylor Series ◽  
Fredholm Integral Equations ◽  
Algebraic Equations ◽  
Numerical Examples ◽  
Hybrid Functions ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method to solve nonlinear Fredholm integral equations of second kind is presented in this work. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Taylor series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of algebraic equations. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

scholarly journals An Appropriate Numerical Method for Solving Nonlinear Volterra-Fredholm Integral Equations

2018 ◽  
Vol 1 (2) ◽  
Author(s):  
Roghayeh Katani 1
Keyword(s):  
Numerical Solution ◽  
Numerical Method ◽  
Integral Equations ◽  
Nonlinear Equations ◽  
Fredholm Integral Equations ◽  
Block Method ◽  
Starting Values ◽  
Linear And Nonlinear

This paper is concerned with the numerical solution of the mixed Volterra-Fredholm integral equations by using a version of the block by block method. This method efficient for linear and nonlinear equations and it avoids the need for spacial starting values. The convergence is proved and finally performance of the method is illustrated by means of some significative examples.

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