scholarly journals Adomian Decomposition Method for a Moving Boundary Problem with Variable Latent Heat

2012 ◽  
Vol 01 (08) ◽  
Author(s):  
Rajeev Singh Kushwaha
Keyword(s):  
Boundary Problem ◽  
Latent Heat ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Moving Boundary Problem ◽  
Adomian Decomposition ◽  
Variable Latent Heat

Legendre wavelet based numerical solution of variable latent heat moving boundary problem

2020 ◽  
Vol 178 ◽  
pp. 485-500
Author(s):  
Jitendra Singh ◽  
Jitendra ◽  
Kabindra Nath Rai
Keyword(s):  
Numerical Solution ◽  
Boundary Problem ◽  
Latent Heat ◽  
Moving Boundary ◽  
Moving Boundary Problem ◽  
Variable Latent Heat

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.

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.

Solution of Fractional Diffusion Equation with a Moving Boundary Condition by Variational Iteration Method and Adomian Decomposition Method

2010 ◽  
Vol 65 (10) ◽  
pp. 793-799 ◽  
Author(s):  
Subir Das ◽  
Subir Rajeev
Keyword(s):  
Boundary Condition ◽  
Diffusion Equation ◽  
Iteration Method ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Variational Iteration Method ◽  
Fractional Diffusion ◽  
Adomian Decomposition ◽  
Moving Boundary Condition

In this paper, the approximate analytic solutions of the mathematical model of time fractional diffusion equation (FDE) with a moving boundary condition are obtained with the help of variational iteration method (VIM) and Adomian decomposition method (ADM). By using boundary conditions, the explicit solutions of the diffusion front and fractional releases in the dimensionless form have been derived. Both mathematical techniques used to solve the problem perform extremely well in terms of efficiency and simplicity. Numerical solutions of the problem show that only a few iterations are needed to obtain accurate approximate analytical solutions. The results obtained are presented graphically.

scholarly journals Approximate Analytic Solutions for the Two-Phase Stefan Problem Using the Adomian Decomposition Method

2014 ◽  
Vol 2014 ◽  
pp. 1-6 ◽  
Author(s):  
Xiao-Ying Qin ◽  
Yue-Xing Duan ◽  
Mao-Ren Yin
Keyword(s):  
Stefan Problem ◽  
Decomposition Method ◽  
Moving Boundary ◽  
Adomian Decomposition Method ◽  
Solidification Process ◽  
Analytic Solutions ◽  
Unknown Boundary ◽  
Two Phase ◽  
Metal Solidification ◽  
Adomian Decomposition

An Adomian decomposition method (ADM) is applied to solve a two-phase Stefan problem that describes the pure metal solidification process. In contrast to traditional analytical methods, ADM avoids complex mathematical derivations and does not require coordinate transformation for elimination of the unknown moving boundary. Based on polynomial approximations for some known and unknown boundary functions, approximate analytic solutions for the model with undetermined coefficients are obtained using ADM. Substitution of these expressions into other equations and boundary conditions of the model generates some function identities with the undetermined coefficients. By determining these coefficients, approximate analytic solutions for the model are obtained. A concrete example of the solution shows that this method can easily be implemented in MATLAB and has a fast convergence rate. This is an efficient method for finding approximate analytic solutions for the Stefan and the inverse Stefan problems.

Sign in / Sign up

Export Citation Format

Share Document