scholarly journals A block by block method with Romberg quadrature for the system of Urysohn type Volterra integral equations

2012 ◽  
Vol 31 (1) ◽  
pp. 191-203 ◽  
Author(s):  
R. Katani ◽  
S. Shahmorad
Keyword(s):  
Integral Equations ◽  
Volterra Integral Equations ◽  
Block Method

scholarly journals A BLOCK BY BLOCK METHOD FOR SOLVING SYSTEM OF VOLTERRA INTEGRAL EQUATIONS WITH CONTINUOUS AND ABEL KERNELS

2015 ◽  
Vol 20 (6) ◽  
pp. 737-753 ◽  
Author(s):  
Roghayeh Katani ◽  
Sedaghat Shahmorad
Keyword(s):  
Integral Equations ◽  
Homotopy Perturbation Method ◽  
Radial Basis Function Network ◽  
Volterra Integral Equations ◽  
Block Method ◽  
Homotopy Perturbation ◽  
Network Method ◽  
Abel Integral Equations ◽  
The Given ◽  
Function Network

Abstract The aim of the present paper is to introduce a block by block method for solving system of nonlinear Volterra integral equations with continuous kernels and system of Abel integral equations. We prove convergence of the method and show that its convergence order is at least six. To illustrate performance of the method, numerical experiments are presented and they are compared with HPM (Homotopy Perturbation Method) and RBFN (Radial Basis Function Network) method. The given results demonstrate remarkable ability of the proposed method.

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