Novel Methods for Solving Linear and Nonlinear Integral Equations

2018 ◽  
Author(s):  
Santanu Saha Ray ◽  
Prakash Kumar Sahu
Keyword(s):  
Integral Equations ◽  
Nonlinear Integral Equations ◽  
Linear And Nonlinear ◽  
Novel Methods

scholarly journals APPLICATION OF THE HOMOTOPY ANALYSIS METHOD FOR SOLVING THE SYSTEMS OF LINEAR AND NONLINEAR INTEGRAL EQUATIONS

2016 ◽  
Vol 21 (3) ◽  
pp. 350-370 ◽  
Author(s):  
Rafal Brociek ◽  
Edyta Hetmaniok ◽  
Jaros law Matlak ◽  
Damian Slota
Keyword(s):  
Approximate Solution ◽  
Integral Equations ◽  
Homotopy Analysis Method ◽  
System Of Equations ◽  
Analysis Method ◽  
Nonlinear Integral Equations ◽  
Function Series ◽  
Partial Sum ◽  
Homotopy Analysis ◽  
Linear And Nonlinear

In this paper we indicate some applications of homotopy analysis method for solving the systems of linear and nonlinear integral equations. The method is based on the concept of creating function series. If the series converges, its sum is the solution of this system of equations. The paper presents conditions to ensure the convergence of this series and estimation of the error of approximate solution obtained when the partial sum of the series is used. Application of the method will be illustrated by examples.

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