Solution Non Linear Partial Differential Equations By ZMA Decomposition Method

2021 ◽  
Vol 20 ◽  
pp. 712-716
Author(s):  
Zainab Mohammed Alwan
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Integral Transformation ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Linear Partial Differential Equations ◽  
Adomian Decomposition

In this survey, viewed integral transformation (IT) combined with Adomian decomposition method (ADM) as ZMA- transform (ZMAT) coupled with (ADM) in which said ZMA decomposition method has been utilized to solve nonlinear partial differential equations (NPDE's).This work is very useful for finding the exact solution of (NPDE's) and this result is more accurate obtained with compared the exact solution obtained in the literature.

Numerical Solution of Fractional Partial Differential Equations by Discrete Adomian Decomposition Method

2014 ◽  
Vol 6 (01) ◽  
pp. 107-119 ◽  
Author(s):  
D. B. Dhaigude ◽  
Gunvant A. Birajdar
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Diffusion Equation ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Fractional Partial Differential Equations ◽  
Partial Differential ◽  
Discrete Schrödinger Equation ◽  
Adomian Decomposition

AbstractIn this paper we find the solution of linear as well as nonlinear fractional partial differential equations using discrete Adomian decomposition method. Here we develop the discrete Adomian decomposition method to find the solution of fractional discrete diffusion equation, nonlinear fractional discrete Schrodinger equation, fractional discrete Ablowitz-Ladik equation and nonlinear fractional discrete Burger’s equation. The obtained solution is verified by comparison with exact solution whenα= 1.

scholarly journals Solution of Nonlinear Partial Differential Equations by Mixture Adomian Decomposition Method and Sumudu Transform

2021 ◽  
Author(s):  
Tarig M. Elzaki ◽  
Shams E. Ahmed
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Sumudu Transform

This chapter is fundamentally centering on the application of the Adomian decomposition method and Sumudu transform for solving the nonlinear partial differential equations. It has instituted some theorems, definitions, and properties of Adomian decomposition and Sumudu transform. This chapter is an elegant combination of the Adomian decomposition method and Sumudu transform. Consequently, it provides the solution in the form of convergent series, then, it is applied to solve nonlinear partial differential equations.

scholarly journals Numerical Solution of Coupled System of Nonlinear Partial Differential Equations Using Laplace-Adomian Decomposition Method

2016 ◽  
Vol 12 (8) ◽  
pp. 6530-6544
Author(s):  
Mohamed S M. Bahgat
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Coupled System ◽  
Decomposition Methods ◽  
Partial Differential ◽  
Adomian Decomposition

Aim of the paper is to investigate applications of Laplace Adomian Decomposition Method (LADM) on nonlinear physical problems. Some coupled system of non-linear partial differential equations (NLPDEs) are considered and solved numerically using LADM. The results obtained by LADM are compared with those obtained by standard and modified Adomian Decomposition Methods. The behavior of the numerical solution is shown through graphs. It is observed that LADM is an effective method with high accuracy with less number of components.

scholarly journals An accelerated solution for some classes of nonlinear partial differential equations

2021 ◽  
Vol 29 (1) ◽  
Author(s):  
I. L. El-Kalla ◽  
E. M. Mohamed ◽  
H. A. A. El-Saka
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Series Solution ◽  
Nonlinear Partial Differential Equations ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Numerical Examples ◽  
Adomian Decomposition

AbstractIn this paper, we apply an accelerated version of the Adomian decomposition method for solving a class of nonlinear partial differential equations. This version is a smart recursive technique in which no differentiation for computing the Adomian polynomials is needed. Convergence analysis of this version is discussed, and the error of the series solution is estimated. Some numerical examples were solved, and the numerical results illustrate the effectiveness of this version.

scholarly journals Adomian Decomposition Method with Modified Bernstein Polynomials for Solving Ordinary and Partial Differential Equations

2018 ◽  
Vol 2018 ◽  
pp. 1-9 ◽  
Author(s):  
Ahmed Farooq Qasim ◽  
Ekhlass S. AL-Rawi
Keyword(s):  
Exact Solution ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Bernstein Polynomials ◽  
Adomian Decomposition Method ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Productive System ◽  
Linear And Nonlinear

In this paper, we used Bernstein polynomials to modify the Adomian decomposition method which can be used to solve linear and nonlinear equations. This scheme is tested for four examples from ordinary and partial differential equations; furthermore, the obtained results demonstrate reliability and activity of the proposed technique. This strategy gives a precise and productive system in comparison with other traditional techniques and the arrangements methodology is extremely straightforward and few emphasis prompts high exact solution. The numerical outcomes showed that the acquired estimated solutions were in appropriate concurrence with the correct solution.

scholarly journals Numerical solution of Drinfeld–Sokolov–Wilso system by using modified Adomian decomposition method

2021 ◽  
Vol 23 (1) ◽  
pp. 590
Author(s):  
Badran Jasim Salim ◽  
Oday Ahmed Jasim ◽  
Zeiad Yahya Ali
Keyword(s):  
Genetic Algorithm ◽  
Exact Solution ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Linear Partial Differential Equations ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Optimal Value ◽  
Mean Square Errors

<p class="Char">In this paper, the modified Adomian decomposition method (MADM) is usedto solve different types of differential equations, one of the numerical analysis methods for solving non linear partial differential equations (Drinfeld–Sokolov–Wilson system) and short (DSWS) that occur in shallow water flows. A Genetic Algorithm was used to find the optimal value for the parameter (a). We numerically solved the system (DSWS) and compared the result to the exact solution. When the value of it is low and close to zero, the MADM provides an excellent approximation to the exact solution. As well as the lower value of leads to the numerical algorithm of (MADM) approaching the real solution.  Finally, found the optimal value when a=-10 by using the Genetic Algorithm (G-MADM). All the computations were carried out with the aid of Maple 18 and Matlab to find the parameter value (a) by using the genetic algorithm as well as to figures drawing. The errors in this paper resulted from cut errors and mean square errors.</p>

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