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 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.

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 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.

Sign in / Sign up

Export Citation Format

Share Document