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Paper Information

Journal:   BULLETIN OF THE IRANIAN MATHEMATICAL SOCIETY   SEPTEMBER 2013 , Volume 39 , Number 4; Page(s) 707 To 724.
 
Paper: 

A NEW BLOCK BY BLOCK METHOD FOR SOLVING TWO-DIMENSIONAL LINEAR AND NONLINEAR VOLTERRA INTEGRAL EQUATIONS OF THE FIRST AND SECOND KINDS

 
 
Author(s):  KATANI R., SHAHMORAD S.*
 
* DEPARTMENT OF APPLIED MATHEMATICS, UNIVERSITY OF TABRIZ, TABRIZ, IRAN
 
Abstract: 

In this paper, we propose a new method for the numerical solution of two-dimensional linear and nonlinear Volterra integral equations of the first and second kinds, which avoids from using starting values. An existence and uniqueness theorem is proved and convergence is verified by using an appropriate variety of the Gronwall inequality. Application of the method is demonstrated for solving the useful telegraph equation.

 
Keyword(s): TWO-DIMENSIONAL VOLTERRA INTEGRAL EQUATIONS, ROMBERG QUADRATURE RULE, BLOCK BY BLOCK METHOD, GRONWALL INEQUALITY
 
References: 
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