The numerical solution of nonlinear two-dimensional Volterra–Fredholm integral equations of the second kind based on the radial basis functions approximation with error analysis

2017 ◽  
Vol 293 ◽  
pp. 545-554 ◽  
Author(s):  
H. Laeli Dastjerdi ◽  
M. Nili Ahmadabadi
Keyword(s):  
Error Analysis ◽  
Numerical Solution ◽  
Integral Equations ◽  
Radial Basis Functions ◽  
Basis Functions ◽  
Fredholm Integral Equations ◽  
Two Dimensional ◽  
Radial Basis

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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