Solving nonlinear Fredholm integral equations with PQWs in complex plane

2021 ◽  
Vol 11 (1) ◽  
pp. 18
Author(s):  
M. Erfanian ◽  
M. Gachpazan ◽  
H. Beiglo
Keyword(s):  
Integral Equations ◽  
Complex Plane ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations

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 of Block-Pulse Functions and Chebyshev Polynomials

2011 ◽  
Vol 2011 ◽  
pp. 1-11 ◽  
Author(s):  
Changqing Yang
Keyword(s):  
Integral Equations ◽  
Chebyshev Polynomials ◽  
Mathematical Physics ◽  
Fredholm Integral Equations ◽  
Chebyshev Series ◽  
Fredholm Type ◽  
Numerical Examples ◽  
Block Pulse Functions ◽  
Hybrid Function ◽  
Nonlinear Fredholm Integral Equations

A numerical method for solving nonlinear Fredholm integral equations of second kind is proposed. The Fredholm-type equations, which have many applications in mathematical physics, are then considered. The method is based upon hybrid function approximate. The properties of hybrid of block-pulse functions and Chebyshev series are presented and are utilized to reduce the computation of nonlinear Fredholm integral equations to a system of nonlinear. Some numerical examples are selected to illustrate the effectiveness and simplicity of the method.

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