Open AccessA comparative analysis for the solution of nonlinear Burgers’ equation
Author(s) -
A. A. Alderremy,
S. Saleem,
F. A. Hendi
Publication year - 2018
Publication title -
journal of integrative neuroscience
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.336
H-Index - 33
eISSN - 1757-448X
pISSN - 0219-6352
DOI - 10.3233/jin-180085
Subject(s) - adomian decomposition method , homotopy analysis method , mathematics , laplace transform , nonlinear system , convergence (economics) , homotopy , burgers' equation , decomposition method (queueing theory) , perturbation (astronomy) , mathematical analysis , partial differential equation , pure mathematics , physics , discrete mathematics , quantum mechanics , economics , economic growth
In this work, a comparative study of seven well-known mathematical techniques for the coupled Burgers' equations is reported. The techniques involve in this comparison are as follows: Laplace transform Adomian decomposition method, Laplace transform homotopy perturbation method, Variational iteration method, Variational iteration decomposition method, Variational iteration homotopy perturbation method, the optimal homotopy asymptotic method, and OHAM with Daftardar-Jafari polynomial. Here we considered a practical example which consists of coupled Burgers' equations with the kinematic viscosity ε=1. Convergence and stability analysis is a major part of this analysis. After a careful observation, it is found that the variational iteration method has faster convergence than all the remaining methods. Adomian decomposition method and Homotopy perturbation method show weaker stability in comparison with other involved techniques.