Approximate solutions to the conformable Rosenau‐Hyman equation using the two‐step Adomian decomposition method with Pad é approximation

2019 ◽  
Vol 43 (13) ◽  
pp. 7632-7639 ◽  
Author(s):  
Ali Akgül ◽  
Aliyu Isa Aliyu ◽  
Mustafa Inc ◽  
Abdullahi Yusuf ◽  
Dumitru Baleanu
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
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 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.

scholarly journals Solution of the space-fractional telegraph equations by using HAM

2015 ◽  
Vol 37 ◽  
pp. 320
Author(s):  
Mehdi Abedi-Varaki ◽  
Shahram Rajabi ◽  
Vahid Ghorbani ◽  
Farzad Hosseinzadeh
Keyword(s):  
Homotopy Analysis Method ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Analysis Method ◽  
Space And Time ◽  
Adomian Decomposition ◽  
Homotopy Analysis ◽  
Telegraph Equations

In this study by using the Homotopy Analysis Method (HAM) obtained approximate solutions for the space and time-fractional telegraph equations. In Caputo sense (Yildirim, 2010)these equations considered. Examples are solved and the obtained results show to be more accurate than Adomian Decomposition Method (ADM) and are more efficient and commodious.

scholarly journals Optimal Parameters for Nonlinear Hirota-Satsuma Coupled KdV System by Using Hybrid Firefly Algorithm with Modified Adomian Decomposition

2020 ◽  
Vol 52 (3) ◽  
pp. 339-352
Author(s):  
Omar Saber Qasim ◽  
Karam Adel Abed ◽  
Ahmed F. Qasim
Keyword(s):  
Exact Solutions ◽  
Hybrid Method ◽  
Decomposition Method ◽  
Firefly Algorithm ◽  
Fitness Function ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Optimal Parameters ◽  
Modified Adomian Decomposition Method ◽  
Adomian Decomposition

In this paper, several parameters of the non-linear Hirota-Satsuma coupled KdV system were estimated using a hybrid between the Firefly Algorithm (FFA) and the Modified Adomian decomposition method (MADM). It turns out that optimal parameters can significantly improve the solutions when using a suitably selected fitness function for this problem. The results obtained show that the approximate solutions are highly compatible with the exact solutions and that the hybrid method FFA_MADM gives higher efficiency and accuracy compared to the classic MADM method.

scholarly journals SOLUTION OF LOCAL FRACTIONAL GENERALIZED FOKKER–PLANCK EQUATION USING LOCAL FRACTIONAL MOHAND ADOMIAN DECOMPOSITION METHOD

Fractals ◽  
2021 ◽  
Author(s):  
SAAD ALTHOBAITI ◽  
RAVI SHANKER DUBEY ◽  
JYOTI GEETESH PRASAD
Keyword(s):  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Planck Equation ◽  
Approximate Solutions ◽  
Simple Approach ◽  
Graphical Representations ◽  
Fokker Planck Equation ◽  
Adomian Decomposition ◽  
Computational Work ◽  
Fokker Planck

In this paper, we solve the local fractional generalized Fokker–Planck equation. To solve the problem, local fractional Mohand transform with Adomian decomposition method is introduced due to its simple approach and less computational work. Furthermore, for the applicability of the technique, we illustrate some examples and their exact or approximate solutions with their graphical representations.

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 Mathematical Analysis of a Reactive Viscous Flow through a Channel Filled with a Porous Medium

2016 ◽  
Vol 2016 ◽  
pp. 1-8 ◽  
Author(s):  
Samuel O. Adesanya ◽  
J. A. Falade ◽  
J. C. Ukaegbu ◽  
K. S. Adekeye
Keyword(s):  
Porous Medium ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Temperature Fields ◽  
Bejan Number ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Velocity And Temperature Fields ◽  
Fluid Parameters

An investigation has been carried out to study entropy generation in a viscous, incompressible, and reactive fluid flowing steadily through a channel with porous materials. Approximate solutions for both velocity and temperature fields are obtained by using a rapidly convergent Adomian decomposition method (ADM). These solutions are then used to determine the heat irreversibility and Bejan number of the problem. Variations of other important fluid parameters are conducted, presented graphically, and discussed.

scholarly journals The Adomian Decomposition Method for Solving a Moving Boundary Problem Arising from the Diffusion of Oxygen in Absorbing Tissue

2014 ◽  
Vol 2014 ◽  
pp. 1-7
Author(s):  
Lazhar Bougoffa
Keyword(s):  
Oxygen Diffusion ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Approximate Analytical Solution ◽  
Adomian Decomposition Method ◽  
Approximate Solutions ◽  
Diffusion Problem ◽  
Moving Boundary Problem ◽  
Resolution Method ◽  
Adomian Decomposition

This paper begins by giving the results obtained by the Crank-Gupta method and Gupta-Banik method for the oxygen diffusion problem in absorbing tissue, and then we propose a new resolution method for this problem by the Adomian decomposition method. An approximate analytical solution is obtained, which is demonstrated to be quite accurate by comparison with the numerical and approximate solutions obtained by Crank and Gupta. The study confirms the accuracy and efficiency of the algorithm for analytic approximate solutions of this problem.

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