Analytical approximate solution of the cooling problem by Adomian decomposition method

2009 ◽  
Vol 14 (2) ◽  
pp. 462-472 ◽  
Author(s):  
Ebrahim Alizadeh ◽  
Kurosh Sedighi ◽  
Mousa Farhadi ◽  
H.R. Ebrahimi-Kebria
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Analytical Approximate Solution ◽  
Adomian Decomposition

scholarly journals A note on time-fractional Navier–Stokes equation and multi-Laplace transform decomposition method

2020 ◽  
Vol 2020 (1) ◽  
Author(s):  
Hassan Eltayeb ◽  
Imed Bachar ◽  
Yahya T. Abdalla
Keyword(s):  
Numerical Simulation ◽  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Navier Stokes ◽  
Two Dimensional ◽  
Navier Stokes Equation ◽  
Adomian Decomposition ◽  
Stokes Problems

Abstract In this study, the double Laplace Adomian decomposition method and the triple Laplace Adomian decomposition method are employed to solve one- and two-dimensional time-fractional Navier–Stokes problems, respectively. In order to examine the applicability of these methods some examples are provided. The presented results confirm that the proposed methods are very effective in the search of exact and approximate solutions for the problems. Numerical simulation is used to sketch the exact and approximate solution.

scholarly journals Approximate Method for Solving the Linear Fuzzy Delay Differential Equations

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
S. Narayanamoorthy ◽  
T. L. Yookesh
Keyword(s):  
Differential Equation ◽  
Exact Solution ◽  
Approximate Solution ◽  
Differential Equations ◽  
Approximate Method ◽  
Delay Differential Equations ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Adomian Decomposition ◽  
Delay Differential

We propose an algorithm of the approximate method to solve linear fuzzy delay differential equations using Adomian decomposition method. The detailed algorithm of the approach is provided. The approximate solution is compared with the exact solution to confirm the validity and efficiency of the method to handle linear fuzzy delay differential equation. To show this proper features of this proposed method, numerical example is illustrated.

scholarly journals Approximate solution of nonlinear ordinary differential equation using ZZ decomposition method

2020 ◽  
Vol 4 (1) ◽  
pp. 448-455
Author(s):  
Mulugeta Andualem ◽  
◽  
Atinafu Asfaw ◽  
Keyword(s):  
Differential Equation ◽  
Ordinary Differential Equation ◽  
Approximate Solution ◽  
Initial Value Problems ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Nonlinear Ordinary Differential Equation ◽  
Initial Value ◽  
Transform Method ◽  
Adomian Decomposition

Nonlinear initial value problems are somewhat difficult to solve analytically as well as numerically related to linear initial value problems as their variety of natures. Because of this, so many scientists still searching for new methods to solve such nonlinear initial value problems. However there are many methods to solve it. In this article we have discussed about the approximate solution of nonlinear first order ordinary differential equation using ZZ decomposition method. This method is a combination of the natural transform method and Adomian decomposition method.

scholarly journals Accurate Approximate Solution of Ambartsumian Delay Differential Equation via Decomposition Method

2019 ◽  
Vol 24 (1) ◽  
pp. 7 ◽  
Author(s):  
Abdelhalim Ebaid ◽  
Asmaa Al-Enazi ◽  
Bassam Z. Albalawi ◽  
Mona D. Aljoufi
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Surface Brightness ◽  
Milky Way ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Canonical Forms ◽  
Exponential Functions ◽  
Adomian Decomposition ◽  
Delay Differential

The Ambartsumian delay equation is used in the theory of surface brightness in the Milky way. The Adomian decomposition method (ADM) is applied in this paper to solve this equation. Two canonical forms are implemented to obtain two types of the approximate solutions. The first solution is provided in the form of a power series which agrees with the solution in the literature, while the second expresses the solution in terms of exponential functions which is viewed as a new solution. A rapid rate of convergence has been achieved and displayed in several graphs. Furthermore, only a few terms of the new approximate solution (expressed in terms of exponential functions) are sufficient to achieve extremely accurate numerical results when compared with a large number of terms of the first solution in the literature. In addition, the residual error using a few terms approaches zero as the delay parameter increases, hence, this confirms the effectiveness of the present approach over the solution in the literature.

An Approximate Solution of Muijderman's Model for Performance Calculation of Spiral Grooved Gas Seal

2017 ◽  
Vol 139 (5) ◽  
Author(s):  
Wanjun Xu ◽  
Jiangang Yang
Keyword(s):  
Approximate Solution ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Kutta Method ◽  
Film Pressure ◽  
Runge Kutta Method ◽  
Decomposition Procedure ◽  
Adomian Decomposition ◽  
Runge Kutta ◽  
Performance Calculation

This paper presents an approximate solution of Muijderman's model for compressible spiral grooved gas film. The approximate solution is derived from Muijderman's equations by Adomian decomposition method. The obtained approximate solution expresses the gas film pressure as a function of the gas film radius. The traditional Runge–Kutta method is avoided. The accuracy of the approximate solution is acceptable, and it brings convenience for performance calculation of spiral grooved gas seal. A complete Adomian decomposition procedure of Muijderman's equations is presented. The approximate solution is validated with published results.

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.

Solutions of the modified Kawahara equation with time-and space-fractional derivatives

2016 ◽  
Vol 7 (1) ◽  
pp. 10 ◽  
Author(s):  
M. Safavi ◽  
A. A. Khajehnasiri
Keyword(s):  
Approximate Solution ◽  
Fractional Differential Equations ◽  
Decomposition Method ◽  
Fractional Derivatives ◽  
Adomian Decomposition Method ◽  
Time And Space ◽  
Kawahara Equation ◽  
Numerical Examples ◽  
Adomian Decomposition ◽  
Fractional Differential

In this paper, we consider fractional differential equations (FDEs), specially modified Kawahara equation with time and space fractional derivatives, also we use Adomian decomposition method (ADM) to approximate the exact solutions of this equation. The ADM method converts the FKEs to an iterated formula that approximate solution is computable. The numerical examples illustrate efficiency and accuracy of the proposed method.

scholarly journals Adomian Decomposition Method Combined with Padé Approximation and Laplace Transform for Solving a Model of HIV Infection of CD4+T Cells

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Fang Chen ◽  
Qing-Quan Liu
Keyword(s):  
T Cells ◽  
Approximate Solution ◽  
Hiv Infection ◽  
Laplace Transform ◽  
Numerical Experiments ◽  
Decomposition Method ◽  
Padé Approximation ◽  
Adomian Decomposition Method ◽  
Pade Approximation ◽  
Adomian Decomposition

The classical Adomian decomposition method (ADM) is implemented to solve a model of HIV infection of CD4+T cells. The results indicate that the approximate solution by using the ADM is the same as that by using the Laplace ADM, but it can be obtained in a more efficient way. We also use Padé approximation and Laplace transform as a posttreatment technique to obtain the result of the ADM. The advantage of the posttreatment is illustrated by numerical experiments.

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