Modification of Sumudu transform "Elzaki transform" and adomian decomposition method

2015 ◽  
Vol 9 ◽  
pp. 603-611
Author(s):  
Tarig M. Elzaki ◽  
Sadah A. Alkhateeb
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Sumudu Transform

Modified Sumudu Decomposition Method for Solving Lane-Emden-Fowler Type Systems

2021 ◽  
Vol 20 ◽  
pp. 446-454
Author(s):  
Chokchai Viriyapong ◽  
Nongluk Viriyapong
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Type Systems ◽  
Singular Equations ◽  
Modified Method ◽  
Adomian Decomposition ◽  
Sumudu Transform

In this paper, the Sumudu decomposition method (SDM) is modified and applied to solve systems of singular equations of the Lane-Emden-Fowler type. The proposed method is based on the application of Sumudu transform and Adomian decomposition method. Some illustrative examples are given to demonstrate the efficiency of the proposed technique. The results show that the modified method is simple and effective

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 Application of Sumudu Decomposition Method to Solve Nonlinear System Volterra Integrodifferential Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Hassan Eltayeb ◽  
Adem Kılıçman ◽  
Said Mesloub
Keyword(s):  
Decomposition Method ◽  
Close Agreement ◽  
Nonlinear Term ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Integrodifferential Equations ◽  
Adomian Polynomials ◽  
Adomian Decomposition ◽  
Present Technique ◽  
Sumudu Transform

We develop a method to obtain approximate solutions for nonlinear systems of Volterra integrodifferential equations with the help of Sumudu decomposition method (SDM). The technique is based on the application of Sumudu transform to nonlinear coupled Volterra integrodifferential 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 which were obtained with the help of Adomian decomposition method (ADM).

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 On Convergence Analysis and Analytical Solutions of the Conformable Fractional Fitzhugh–Nagumo Model Using the Conformable Sumudu Decomposition Method

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 243
Author(s):  
Suliman Alfaqeih ◽  
Emine Mısırlı
Keyword(s):  
Convergence Analysis ◽  
Decomposition Method ◽  
Fixed Point Theory ◽  
Adomian Decomposition Method ◽  
Nerve Impulse ◽  
Point Theory ◽  
Easy Method ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Mathematica Software

The current article studied a nonlinear transmission of the nerve impulse model, the Fitzhugh–Nagumo (FN) model, in the conformable fractional form with an efficient analytical approach based on a combination of conformable Sumudu transform and the Adomian decomposition method. Convergence analysis and error analysis were also carried out based on the Banach fixed point theory. We also provided some examples to support our results. The results obtained revealed that the presented approach is very fantastic, effective, reliable, and is an easy method to handle specific problems in various fields of applied sciences and engineering. The Mathematica software carried out all the computations and graphics in this paper.

scholarly journals Sumudu Decomposition Method for Solving Fractional Bratu-Type Differential Equations

2020 ◽  
Vol 12 (4) ◽  
pp. 585-605
Author(s):  
N. B. Manjare ◽  
H. T. Dinde
Keyword(s):  
Differential Equation ◽  
Decomposition Method ◽  
Series Solution ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Convergent Series ◽  
Approximate Analytical Solutions ◽  
Adomian Decomposition ◽  
Sumudu Transform ◽  
Type Differential Equation

The purpose of this paper is to introduce Sumudu decomposition method for solving Fractional Bratu-type differential equation. This method is a combination of the Sumudu transform and Adomian decomposition method. The fractional derivative is described in the Caputo sense. The Sumudu decomposition method is applied to obtain approximate analytical solution of non-linear Fractional Bratu-type differential equation. A novel combination of Sumudu transform and Adomian decomposition provides approximate solution in the form of infinite convergent series solution. The behavior of approximate analytical solutions and exact solutions for different values of α are plotted graphically. The results acquired from Sumudu decomposition method indicates that the proposed method is very well founded, suitable and effective. Finally, some numerical examples are given to illustrate the efficiency and applicability of our method.

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.

SOLUTION OF NEWEL-WHITEHEAD-SEGEL EQUATION USING CONFORMABLE FRACTIONAL SUMUDU DECOMPOSITION METHOD

2021 ◽  
Vol 21 (2) ◽  
pp. 479-486
Author(s):  
MOHAMED ELARBI BENATTIA ◽  
KACEM BELGHABA
Keyword(s):  
Numerical Method ◽  
Analytical Solutions ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Initial Condition ◽  
Adomian Decomposition ◽  
Sumudu Transform

In the present paper, a numerical method is proposed to solve the time fractional Newel-Whitead-Segel equation subject to initial condition. This method is based d on the unification of conformable Sumudu transform (CST) and Adomian decomposition method (ADM), and then it is used to find the analytical solutions of linear-nonlinear fractional PDE’s. The test examples are given for illustration

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