scholarly journals Convergence Analysis of Parabolic Basis Functions for Solving Systems of Linear and Nonlinear Fredholm Integral Equations

2017 ◽  
Vol 41 ◽  
pp. 787-796 ◽  
Author(s):  
Yousef JAFARZADEH ◽  
Bagher KERAMATI
Keyword(s):  
Convergence Analysis ◽  
Integral Equations ◽  
Basis Functions ◽  
Fredholm Integral Equations ◽  
Nonlinear Fredholm Integral Equations ◽  
Linear And Nonlinear ◽  
Parabolic Basis

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 Exponential Convergence for Numerical Solution of Integral Equations Using Radial Basis Functions

2014 ◽  
Vol 2014 ◽  
pp. 1-9
Author(s):  
Zakieh Avazzadeh ◽  
Mohammad Heydari ◽  
Wen Chen ◽  
G. B. Loghmani
Keyword(s):  
Integral Equations ◽  
Radial Basis Functions ◽  
Exponential Convergence ◽  
Higher Dimensions ◽  
Basis Functions ◽  
Fredholm Integral Equations ◽  
Urysohn Integral Equations ◽  
Radial Basis ◽  
Ill Posed ◽  
Linear And Nonlinear

We solve some different type of Urysohn integral equations by using the radial basis functions. These types include the linear and nonlinear Fredholm, Volterra, and mixed Volterra-Fredholm integral equations. Our main aim is to investigate the rate of convergence to solve these equations using the radial basis functions which have normic structure that utilize approximation in higher dimensions. Of course, the use of this method often leads to ill-posed systems. Thus we propose an algorithm to improve the results. Numerical results show that this method leads to the exponential convergence for solving integral equations as it was already confirmed for partial and ordinary differential equations.

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