Solution of jamming transition problem using adomian decomposition method

2018 ◽  
Vol 35 (5) ◽  
pp. 1950-1964 ◽  
Author(s):  
Erman Şentürk ◽  
Safa Bozkurt Coşkun ◽  
Mehmet Tarık Atay
Keyword(s):  
Decomposition Method ◽  
Numerical Solutions ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Numerical Function ◽  
Content Type ◽  
Jamming Transition ◽  
Transition Problem ◽  
Adomian Decomposition ◽  
Highly Nonlinear

Purpose The purpose of the study is to obtain an analytical approximate solution for jamming transition problem (JTP) using Adomian decomposition method (ADM). Design/methodology/approach In this study, the jamming transition is presented as a result of spontaneous deviations of headway and velocity that is caused by the acceleration/breaking rate to be higher than the critical value. Dissipative dynamics of traffic flow can be represented within the framework of the Lorenz scheme based on the car-following model in the one-lane highway. Through this paper, an analytical approximation for the solution is calculated via ADM that leads to a solution for headway deviation as a function of time. Findings A highly nonlinear differential equation having no exact solution due to JTP is considered and headway deviation is obtained implementing a number of different initial conditions. The results are discussed and compared with the available data in the literature and numerical solutions obtained from a built-in numerical function of the mathematical software used in the study. The advantage of using ADM for the problem is presented in the study and discussed on the basis of the results produced by the applied method. Originality/value This is the first study to apply ADM to JTP.

scholarly journals Analytic Fuzzy Formulation of a Time-Fractional Fornberg–Whitham Model with Power and Mittag–Leffler Kernels

2021 ◽  
Vol 5 (3) ◽  
pp. 113 ◽  
Author(s):  
Saima Rashid ◽  
Rehana Ashraf ◽  
Ahmet Ocak Akdemir ◽  
Manar A. Alqudah ◽  
Thabet Abdeljawad ◽  
...  
Keyword(s):  
Fractional Derivative ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Algorithmic Approach ◽  
Closed Form Solutions ◽  
Adomian Decomposition ◽  
Fractional Orders

This manuscript assesses a semi-analytical method in connection with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). Moreover, we use the aforesaid strategy to address the time-fractional Fornberg–Whitham equation (FWE) under gH-differentiability by employing different initial conditions (IC). Several algebraic aspects of the fuzzy Caputo fractional derivative (CFD) and fuzzy Atangana–Baleanu (AB) fractional derivative operator in the Caputo sense, with respect to the Elzaki transform, are presented to validate their utilities. Apart from that, a general algorithm for fuzzy Caputo and AB fractional derivatives in the Caputo sense is proposed. Some illustrative cases are demonstrated to understand the algorithmic approach of FWE. Taking into consideration the uncertainty parameter ζ∈[0,1] and various fractional orders, the convergence and error analysis are reported by graphical representations of FWE that have close harmony with the closed form solutions. It is worth mentioning that the projected approach to fuzziness is to verify the supremacy and reliability of configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

A reliable convergent Adomian decomposition method for heat transfer through extended surfaces

2018 ◽  
Vol 28 (11) ◽  
pp. 2551-2566 ◽  
Author(s):  
Mustafa Turkyilmazoglu
Keyword(s):  
Heat Transfer ◽  
Decomposition Method ◽  
Adomian Decomposition Method ◽  
Solution Procedure ◽  
Published Data ◽  
Content Type ◽  
Fin Efficiency ◽  
Nonlinear Properties ◽  
Adomian Decomposition ◽  
Highly Nonlinear

PurposeThis paper aims to revisite the traditional Adomian decomposition method frequently used for the solution of highly nonlinear extended surface problems in order to understand the heat transfer enhancement phenomenon. It is modified to include a parameter adjusting and controlling the convergence of the resulting Adomian series.Design/methodology/approachIt is shown that without such a convergence control parameter, some of the published data in the literature concerning the problem are lacking accuracy or the worst is untrustful. With the proposed amendment over the classical Adomian decomposition method, it is easy to gain the range of parameters guaranteeing the convergence of the Adomian series.FindingsWith the presented improvement, the reliable behavior of the fin tip temperature and the fin efficiency of the most interested from practical perspective are easily predicted.Originality/valueThe relevant future studies involving the fin problems covering many physical nonlinear properties must be properly treated as guided in this paper, while the Adomian decomposition method is adopted for the solution procedure.

scholarly journals A Novel Treatment of Fuzzy Fractional Swift–Hohenberg Equation for a Hybrid Transform within the Fractional Derivative Operator

2021 ◽  
Vol 5 (4) ◽  
pp. 209
Author(s):  
Saima Rashid ◽  
Rehana Ashraf ◽  
Fatimah S. Bayones
Keyword(s):  
Fractional Derivative ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Integral Transform ◽  
Initial Conditions ◽  
Adomian Decomposition Method ◽  
Initial Value ◽  
Adomian Decomposition ◽  
In Series ◽  
Fractional Orders

This article investigates the semi-analytical method coupled with a new hybrid fuzzy integral transform and the Adomian decomposition method via the notion of fuzziness known as the Elzaki Adomian decomposition method (briefly, EADM). In addition, we apply this method to the time-fractional Swift–Hohenberg equation (SHe) with various initial conditions (IC) under gH-differentiability. Some aspects of the fuzzy Caputo fractional derivative (CFD) with the Elzaki transform are presented. Moreover, we established the general formulation and approximate findings by testing examples in series form of the models under investigation with success. With the aid of the projected method, we establish the approximate analytical results of SHe with graphical representations of initial value problems by inserting the uncertainty parameter 0≤℘≤1 with different fractional orders. It is expected that fuzzy EADM will be powerful and accurate in configuring numerical solutions to nonlinear fuzzy fractional partial differential equations arising in physical and complex structures.

Numerical solution of large deflection beams by using the Laplace Adomian decomposition method

2021 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Ming-Xian Lin ◽  
Chia-Hsiang Tseng ◽  
Chao Kuang Chen
Keyword(s):  
Decomposition Method ◽  
Large Deflection ◽  
Adomian Decomposition Method ◽  
Nonlinear Behavior ◽  
Bernoulli Beam ◽  
Rapid Convergence ◽  
Content Type ◽  
Adomian Decomposition ◽  
Euler Bernoulli Beam ◽  
Better Than

PurposeThis paper presents the problems using Laplace Adomian decomposition method (LADM) for investigating the deformation and nonlinear behavior of the large deflection problems on Euler-Bernoulli beam.Design/methodology/approachThe governing equations will be converted to characteristic equations based on the LADM. The validity of the LADM has been confirmed by comparing the numerical results to different methods.FindingsThe results of the LADM are found to be better than the results of Adomian decomposition method (ADM), due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms. LADM are presented for two examples for large deflection problems. The results obtained from example 1 shows the effects of the loading, horizontal parameters and moment parameters. Example 2 demonstrates the point loading and point angle influence on the Euler-Bernoulli beam.Originality/valueThe results of the LADM are found to be better than the results of ADM, due to this method's rapid convergence and accuracy to obtain the solutions by using fewer iterative terms.

Adomian decomposition method to magnetohydrodynamics natural convection heat generating/absorbing slip flow through a porous medium

2019 ◽  
Vol 15 (3) ◽  
pp. 673-684 ◽  
Author(s):  
Abiodun O. Ajibade ◽  
Jeremiah Jerry Gambo
Keyword(s):  
Porous Medium ◽  
Natural Convection ◽  
Decomposition Method ◽  
Slip Flow ◽  
Adomian Decomposition Method ◽  
Convection Heat ◽  
Content Type ◽  
Adomian Decomposition ◽  
Flow Through ◽  
Effect Parameter

Purpose The purpose of this paper is to analyze magnetohydrodynamics fully developed natural convection heat-generating/absorbing slip flow through a porous medium. Adomian decomposition method was applied to find the solutions to the problem. Design/methodology/approach In this study, Adomian decomposition method was used. Findings Results show that heat generation parameter enhanced the temperature and velocity of the fluid in the annulus. Moreover, slip effect parameter increases the velocity of the fluid. Originality/value Originality is in the application of Adomian decomposition method which allowed the slip at interface.

scholarly journals Computational and Numerical Solutions for 2+1-Dimensional Integrable Schwarz–Korteweg–de Vries Equation with Miura Transform

Complexity ◽  
2020 ◽  
Vol 2020 ◽  
pp. 1-13
Author(s):  
Raghda A. M. Attia ◽  
S. H. Alfalqi ◽  
J. F. Alzaidi ◽  
Mostafa M. A. Khater ◽  
Dianchen Lu
Keyword(s):  
Solitary Waves ◽  
Decomposition Method ◽  
Numerical Solutions ◽  
Vries Equation ◽  
Adomian Decomposition Method ◽  
Simplest Equation Method ◽  
Adomian Decomposition ◽  
Tanh Method ◽  
De Vries ◽  
Parameter Values

This paper investigates the analytical, semianalytical, and numerical solutions of the 2+1–dimensional integrable Schwarz–Korteweg–de Vries (SKdV) equation. The extended simplest equation method, the sech-tanh method, the Adomian decomposition method, and cubic spline scheme are employed to obtain distinct formulas of solitary waves that are employed to calculate the initial and boundary conditions. Consequently, the numerical solutions of this model can be investigated. Moreover, their stability properties are also analyzed. The solutions obtained by means of these techniques are compared to unravel relations between them and their characteristics illustrated under the suitable choice of the parameter values.

Adomian Decomposition Method for Approximating the Solutions of the Bidirectional Sawada-Kotera Equation

2010 ◽  
Vol 65 (8-9) ◽  
pp. 658-664 ◽  
Author(s):  
Xian-Jing Lai ◽  
Xiao-Ou Cai
Keyword(s):  
Decomposition Method ◽  
Initial Conditions ◽  
Soliton Solutions ◽  
Adomian Decomposition Method ◽  
Nonlinear Problems ◽  
Absolute Error ◽  
Solitary Wave Solutions ◽  
Adomian Polynomials ◽  
Wave Solutions ◽  
Adomian Decomposition

In this paper, the decomposition method is implemented for solving the bidirectional Sawada- Kotera (bSK) equation with two kinds of initial conditions. As a result, the Adomian polynomials have been calculated and the approximate and exact solutions of the bSK equation are obtained by means of Maple, such as solitary wave solutions, doubly-periodic solutions, two-soliton solutions. Moreover, we compare the approximate solution with the exact solution in a table and analyze the absolute error and the relative error. The results reported in this article provide further evidence of the usefulness of the Adomian decomposition method for obtaining solutions of nonlinear problems

scholarly journals The Time-Fractional Coupled-Korteweg-de-Vries Equations

2013 ◽  
Vol 2013 ◽  
pp. 1-8 ◽  
Author(s):  
Abdon Atangana ◽  
Aydin Secer
Keyword(s):  
Decomposition Method ◽  
Homotopy Perturbation Method ◽  
Numerical Solutions ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Analytical Technique ◽  
Adomian Decomposition ◽  
Homotopy Decomposition ◽  
De Vries ◽  
Homotopy Analysis

We put into practice a relatively new analytical technique, the homotopy decomposition method, for solving the nonlinear fractional coupled-Korteweg-de-Vries equations. Numerical solutions are given, and some properties exhibit reasonable dependence on the fractional-order derivatives’ values. The fractional derivatives are described in the Caputo sense. The reliability of HDM and the reduction in computations give HDM a wider applicability. In addition, the calculations involved in HDM are very simple and straightforward. It is demonstrated that HDM is a powerful and efficient tool for FPDEs. It was also demonstrated that HDM is more efficient than the adomian decomposition method (ADM), variational iteration method (VIM), homotopy analysis method (HAM), and homotopy perturbation method (HPM).

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