On the Adomian decomposition method for solving the Stefan problem

2015 ◽  
Vol 25 (4) ◽  
pp. 912-928 ◽  
Author(s):  
Lazhar Bougoffa ◽  
Randolph Rach ◽  
Abdul-Majid Wazwaz ◽  
Jun-Sheng Duan
Keyword(s):  
Latent Heat ◽  
Stefan Problem ◽  
Decomposition Method ◽  
Design Methodology ◽  
Adomian Decomposition Method ◽  
Solution Algorithm ◽  
Content Type ◽  
Analytic Treatment ◽  
Adomian Decomposition ◽  
Variable Latent Heat

Purpose – The purpose of this paper is concerned with a reliable treatment of the classical Stephan problem. The Adomian decomposition method (ADM) is used to carry out the analysis, Moreover, the authors extend the work to examine the Stefan problem with variable latent heat. The study confirms the accuracy and efficiency of the employed method. Design/methodology/approach – The new technique, as presented in this paper in extending the applicability of the ADM, has been shown to be very efficient for solving the Stefan problem. Findings – The Stefan problem with variable latent heat was examined as well. The ADM was effectively used for analytic treatment of the Stefan problem with and without variable latent heat. Originality/value – The paper presents a new solution algorithm for the Stefan problem.

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.

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.

Bioconvective peristaltic flow of a third-grade nanofluid embodying gyrotactic microorganisms in the presence of Cu-blood nanoparticles with permeable walls

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Asha Shivappa Kotnurkar ◽  
Deepa C. Katagi
Keyword(s):  
Design Methodology ◽  
Adomian Decomposition Method ◽  
Peristaltic Flow ◽  
Third Grade ◽  
Nanofluid Flow ◽  
Gyrotactic Microorganisms ◽  
Content Type ◽  
Adomian Decomposition ◽  
Permeable Walls ◽  
Practical Implications

PurposeThe current paper investigates the bioconvective third-grade nanofluid flow containing gyrotactic organisms with Copper-blood nanoparticles in permeable walls.Design/methodology/approachThe equations governing the flow are solved by adopting the Adomian decomposition method.FindingsThe results show that the biconvection Peclet number decreases the density of motile microorganisms, and the Rayleigh number also decreases the velocity profile.Practical implicationsThe present study can be applied to design the higher generation microsystems.Originality/valueTo the best of the authors’ knowledge, no such investigation has been carried out in the literature.

scholarly journals Dynamics Analysis and Synchronous Control of Fractional-Order Entanglement Symmetrical Chaotic Systems

Symmetry ◽  
2021 ◽  
Vol 13 (11) ◽  
pp. 1996
Author(s):  
Tengfei Lei ◽  
Beixing Mao ◽  
Xuejiao Zhou ◽  
Haiyan Fu
Keyword(s):  
Fractional Order ◽  
Decomposition Method ◽  
Chaotic Systems ◽  
Sliding Mode ◽  
Adomian Decomposition Method ◽  
Solution Algorithm ◽  
Fractional Order Systems ◽  
Synchronous Control ◽  
Adomian Decomposition ◽  
Lyapunov Exponent Spectrum

In this paper, the Adomian decomposition method (ADM) semi-analytical solution algorithm is applied to solve a fractional-order entanglement symmetrical chaotic system. The dynamics of the system are analyzed by the Lyapunov exponent spectrum, bifurcation diagrams, poincaré diagrams, and chaos diagrams. The results show that the systems have rich dynamics. Meanwhile, sliding mode synchronizations of fractional-order chaotic systems are investigated theoretically and numerically. The results show the effectiveness of the proposed method and potential application value of fractional-order systems.

Heat dissipation analysis of continuously-moving plate undergoing thermal processing using Laplace Adomian decomposition method

2017 ◽  
Vol 34 (7) ◽  
pp. 2242-2255
Author(s):  
Cha’o Kuang Chen ◽  
Yu-Shen Chang ◽  
Chin-Chia Liu ◽  
Bang-Shiuh Chen
Keyword(s):  
Thermal Processing ◽  
Decomposition Method ◽  
Heat Dissipation ◽  
Temperature Drop ◽  
Adomian Decomposition Method ◽  
Surface Emissivity ◽  
Moving Plate ◽  
Content Type ◽  
Practical Applications ◽  
Adomian Decomposition

Purpose This paper aims to use the Laplace Adomian decomposition method (LADM) to investigate the effects of thermal convection, thermal conduction, surface emissivity and thermal radiation on the heat dissipated by a continuously moving plate undergoing thermal processing. Design/methodology/approach In performing the analysis, it is assumed that the thermal conductivity and surface emissivity of the plate are both temperature-dependent. The accuracy of the LADM solutions is confirmed by comparing the results obtained for the temperature distribution within the plate with those reported in the literature based on the differential transformation method. Findings It is shown that the heat dissipated from the plate reduces as the Peclet number increases. By contrast, the dissipated heat increases as any one of the non-dimensionalized parameters of the system, i.e. Nc, Nr and B, increases. In addition, the temperature drop along the length of the plate reduces as parameter A increases owing to a more rapid heat transfer. Originality/value The results provide a useful source of reference for the choice of suitable materials and cooling fluids in a variety of practical applications.

Numerical solution of Lane-Emden type equations using Adomian decomposition method with unequal step-size partitions

2020 ◽  
Vol ahead-of-print (ahead-of-print) ◽  
Author(s):  
Umesh Umesh ◽  
Manoj Kumar
Keyword(s):  
Differential Equations ◽  
Numerical Solution ◽  
Decomposition Method ◽  
Nonlinear Differential Equations ◽  
Adomian Decomposition Method ◽  
The Other ◽  
Step Size ◽  
Adomian Polynomials ◽  
Content Type ◽  
Adomian Decomposition

Purpose The purpose of this paper is to obtain the highly accurate numerical solution of Lane–Emden-type equations using modified Adomian decomposition method (MADM) for unequal step-size partitions. Design/methodology/approach First, the authors describe the standard Adomian decomposition scheme and the Adomian polynomials for solving nonlinear differential equations. After that, for the fast calculation of the Adomian polynomials, an algorithm is presented based on Duan’s corollary and Rach’s rule. Then, MADM is discussed for the unequal step-size partitions of the domain, to obtain the numerical solution of Lane–Emden-type equations. Moreover, convergence analysis and an error bound for the approximate solution are discussed. Findings The proposed method removes the singular behaviour of the problems and provides the high precision numerical solution in the large effective region of convergence in comparison to the other existing methods, as shown in the tested examples. Originality/value Unlike the other methods, the proposed method does not require linearization or perturbation to obtain an analytical and numerical solution of singular differential equations, and the obtained results are more physically realistic.

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