Extrapolation methods for the numerical solution of nonlinear Fredholm integral equations

2019 ◽  
Vol 31 (1) ◽  
pp. 29-57
Author(s):  
Claude Brezinski ◽  
Michela Redivo-Zaglia
Keyword(s):  
Numerical Solution ◽  
Integral Equations ◽  
Fredholm Integral Equations ◽  
Extrapolation Methods ◽  
Nonlinear Fredholm 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.

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