A Maple program for solving systems of linear and nonlinear integral equations by Adomian decomposition method

2007 ◽  
Vol 2 ◽  
pp. 1425-1432
Author(s):  
J. Biazar ◽  
M. Pourabd
Keyword(s):  
Integral Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Integral Equations ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

scholarly journals Computation of semi-analytical solutions of fuzzy nonlinear integral equations

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Zia Ullah ◽  
Aman Ullah ◽  
Kamal Shah ◽  
Dumitru Baleanu
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Decomposition Method ◽  
Nonlinear Integral Equation ◽  
Adomian Decomposition Method ◽  
Main Theme ◽  
Parametric Form ◽  
Nonlinear Integral Equations ◽  
Adomian Decomposition ◽  
Nonlinear Fredholm Integral Equation

Abstract In this article, we use a fuzzy number in its parametric form to solve a fuzzy nonlinear integral equation of the second kind in the crisp case. The main theme of this article is to find a semi-analytical solution of fuzzy nonlinear integral equations. A hybrid method of Laplace transform coupled with Adomian decomposition method is used to find the solution of the fuzzy nonlinear integral equations including fuzzy nonlinear Fredholm integral equation, fuzzy nonlinear Volterra integral equation, and fuzzy nonlinear singular integral equation of Abel type kernel. We also provide some suitable examples to better understand the proposed method.

scholarly journals A New Modification of Adomian Decomposition Method for Volterra Integral Equations of the Second Kind

2013 ◽  
Vol 2013 ◽  
pp. 1-7 ◽  
Author(s):  
Lie-jun Xie
Keyword(s):  
Integral Equations ◽  
Nonlinear Equations ◽  
Decomposition Method ◽  
Taylor Expansion ◽  
Series Solution ◽  
New Technology ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Adomian Decomposition ◽  
Linear And Nonlinear

We propose a new modification of the Adomian decomposition method for Volterra integral equations of the second kind. By the Taylor expansion of the components apart from the zeroth term of the Adomian series solution, this new technology overcomes the problems arising from the previous decomposition method. The validity and applicability of the new technique are illustrated through several linear and nonlinear equations by comparing with the standard decomposition method and the modified decomposition method. The results obtained indicate that the new modification is effective and promising.

THE ADOMIAN DECOMPOSITION METHOD APPLIED TO THE FUZZY SYSTEM OF FREDHOLM INTEGRAL EQUATIONS OF THE SECOND KIND

2006 ◽  
Vol 14 (01) ◽  
pp. 101-110 ◽  
Author(s):  
S. ABBASBANDY ◽  
T. ALLAHVIRANLOO
Keyword(s):  
Integral Equation ◽  
Integral Equations ◽  
Fredholm Integral Equation ◽  
Fuzzy System ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fredholm Integral Equations ◽  
Extension Principle ◽  
Numerical Example ◽  
Adomian Decomposition

In this work, the Adomian decomposition(AD) method is applied to the Fuzzy system of linear Fredholm integral equations of the second kind(FFIE). First the crisp Fredholm integral equation is solved by AD method and then the crisp solution is fuzzified by extension principle. The proposed algorithm is illustrated by solving a numerical example.

scholarly journals Approximate Solution of Urysohn Integral Equations Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6
Author(s):  
Randhir Singh ◽  
Gnaneshwar Nelakanti ◽  
Jitendra Kumar
Keyword(s):  
Approximate Solution ◽  
Error Analysis ◽  
Integral Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Adomian Decomposition Method ◽  
Numerical Examples ◽  
Recursive Scheme ◽  
Urysohn Integral Equations ◽  
Adomian Decomposition

We apply Adomian decomposition method (ADM) for obtaining approximate series solution of Urysohn integral equations. The ADM provides a direct recursive scheme for solving such problems approximately. The approximations of the solution are obtained in the form of series with easily calculable components. Furthermore, we also discuss the convergence and error analysis of the ADM. Moreover, three numerical examples are included to demonstrate the accuracy and applicability of the method.

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