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.

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.

scholarly journals Application of Sumudu Decomposition Method to Solve Nonlinear System of Partial Differential Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-13 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman
Keyword(s):  
Partial Differential Equations ◽  
Nonlinear System ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Partial Differential ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Sumudu Transform

We develop a method to obtain approximate solutions of nonlinear system of partial differential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled partial differential equations. The nonlinear term can easily be handled with the help of Adomian polynomials. We illustrate this technique with the help of three examples, and results of the present technique have close agreement with approximate solutions obtained with the help of Adomian decomposition method (ADM).

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.

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.

Solution methodology of convection boundary layer problems using Adomian decomposition method

2012 ◽  
Vol 227 (7) ◽  
pp. 1554-1565
Author(s):  
MJ Javanmardi ◽  
K Jafarpur ◽  
M Mahzoon
Keyword(s):  
Boundary Layer ◽  
Partial Differential Equations ◽  
Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Convection Boundary Layer ◽  
Partial Differential ◽  
Adomian Decomposition ◽  
Convection Boundary ◽  
Boundary Layer Problems

Adomian decomposition method has been applied to some convection boundary layer problems. It is shown that the method is excellent in solving nonlinear partial differential equations. Comparison of the results so obtained and those from conventional methods proves the technique to be powerful and to give nearly exact solutions. Since most physical problems are governed by nonlinear ordinary or partial differential equations, application of this method may be advised to simplify the method of solution.

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