Adomian Decomposition Method for Solving the Singularly Perturbed Volterra Integral Equations

2017 ◽  
Vol 6 (2) ◽  
pp. 105-114
Author(s):  
Waleed Al-Hayani ◽  
Omar Mudhar Kashmola
Keyword(s):  
Integral Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Singularly Perturbed ◽  
Adomian Decomposition

scholarly journals Approximate Solution of Systems of Volterra Integral Equations of Second Kind by Adomian Decomposition Method

2015 ◽  
Vol 63 (1) ◽  
pp. 15-18
Author(s):  
Md Shariful Islam ◽  
Mir Shariful Islam ◽  
Md Zavid Iqbal Bangalee ◽  
AFM Khodadad Khan ◽  
Amal Halder
Keyword(s):  
Approximate Solution ◽  
Linear System ◽  
Integral Equations ◽  
Decomposition Method ◽  
Real Life ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Life Problems ◽  
Adomian Decomposition ◽  
Differential And Integral Equations

Real life problems that arise in different branches of science and social science, in the form of differential and integral equations are non-linear in nature. However, methods developed in Mathematics, usually, are suitable for the linear system. In this article, we talk on approximating solution of system of Volterra integral equations of second kind in an analytic way using Adomian decomposition method in Mathematica. DOI: http://dx.doi.org/10.3329/dujs.v63i1.21761 Dhaka Univ. J. Sci. 63(1): 15-18, 2015 (January)

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.

scholarly journals Resolution of system of Volterra integral equations of the first kind by derivation technique and modified decomposition methods

2020 ◽  
Vol 16 (2) ◽  
pp. 23-38
Author(s):  
M. A. Alzhrani ◽  
H. O. Bakodah ◽  
M. Al-Mazmumy
Keyword(s):  
Integral Equations ◽  
Decomposition Method ◽  
Solution Method ◽  
Practical Interest ◽  
Adomian Decomposition Method ◽  
Decomposition Methods ◽  
Volterra Integral Equations ◽  
Adomian Decomposition ◽  
Systems Of Integral Equations

AbstractA solution method for various systems of integral equations of the first kind is presented in this paper. The method starts off by transforming the systems via the application of the Leibnitz’s derivation technique and then employs three different decomposition methods based on the Standard Adomian decomposition method (SADM) for solutions. To demonstrate the efficiency of the proposed method, some illustrative examples are considered and the obtained results indicate that the approach is indeed of practical interest.

scholarly journals Solving Systems of Non-Linear Volterra Integral Equations by Combined Sumudu Transform-Adomian Decomposition Method

2021 ◽  
pp. 252-268
Author(s):  
Lamiaa H. Al-Taee ◽  
Waleed Al-Hayani
Keyword(s):  
Nonlinear Systems ◽  
Exact Solutions ◽  
Integral Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
High Accuracy ◽  
Volterra Integral Equations ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Linear Volterra Integral Equations

     This paper is used for solving component Volterra nonlinear systems by means of the combined Sumudu transform with Adomian decomposition process. We equate the numerical results with the exact solutions to demonstrate the high accuracy of the solution results. The results show that the approach is very straightforward and effective.

scholarly journals The Study for Synchronization between Two Coupled FitzHugh-Nagumo Neurons Based on the Laplace Transform and the Adomian Decomposition Method

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Bin Zhen ◽  
Zigen Song
Keyword(s):  
Laplace Transform ◽  
Integral Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Volterra Integral Equations ◽  
Successive Approximation Method ◽  
External Current ◽  
Synchronization Errors ◽  
Adomian Decomposition ◽  
The Laplace Transform

The synchronization between two coupled FitzHugh-Nagumo (FHN) neurons with or without external current is studied by using the Laplace transform and the Adomian decomposition method. Different from other researches, the synchronization error system is expressed as sets of Volterra integral equations based on the convolution theorem in the Laplace transform. Then, it is easy to analytically obtain the conditions that synchronization errors disappear based on the successive approximation method in integral equation theorem, the correctness of which is verified by numerical simulations. Furthermore, the synchronous dynamics of the two coupled FHN neurons also can be written in the form of Volterra integral equations, which is more convenient to analytically solve by using the Adomian decomposition method. It is found that the occurrence of synchronization between the two FHN neurons only depends on the coupling strength and is irrelevant to the external current. Only synchronous rest state in the two FHN neurons without external current can be achieved, while synchronous spikes appear if the external current is not zero.

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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