Search

Abstract: The aim of this article is to introduce a new approximate method, namely homotopy analysis transform method (HATM) which is a combination of homotopy analysis method (HAM) and Laplace decomposition method (LDM) to provide an analytical approximate solution to Blasius flow equations. The proposed scheme finds the solutions of nonlinear problems without any discretization, restrictive assumptions and avoids the rounding-off errors. The proposed technique solves the nonlinear problems without using Adomian polynomials and He’s polynomials which can be considered as a clear advantage of this new algorithm over decomposition and the homotopy perturbation transform method (HPTM). A good agreement between the obtained solution and some well-known results has been demonstrated. [Copyright &y& Elsevier]

In this article, Laplace decomposition method (LDM) is applied to obtain series solutions of classical Blasius equation. The technique is based on the application of Laplace transform to nonlinear Blasius flow equation. The nonlinear term can easily be handled with the help of Adomian polynomials. The results of the present technique have closed agreement with series solutions obtained with the help of Adomian decomposition method (ADM), variational iterative method (VIM) and homotopy perturbation method (HPM). [ABSTRACT FROM AUTHOR]

This paper carries out the numerical analysis of perturbed optical solitons that are governed by Sasa–Satsuma equation. Laplace–Adomian decomposition is the integration scheme that is implemented to recover bright and dark optical solitons to the model. The surface plots of bright and dark optical solitons are exhibited. The contour plots and error plots are also displayed. The error measure that emerged from the integration scheme is O (1 0 − 7) and is an impressive measure! [ABSTRACT FROM AUTHOR]

The main purpose of this work is to suggest an efficient hybrid computational technique, namely the q-homotopy analysis transform method (q-HATM) to find the solution of the nonlinear time-fractional Zakharov–Kuznetsov (FZK) equation in two dimensions. The uniqueness and convergence analysis of the nonlinear time-FZK equation is presented. The Laplace decomposition method (LDM) is also employed to get the approximate solution of the nonlinear FZK equation. We implemented these techniques on two numerical examples, plotted the solution and compared the absolute error with the variational iteration technique and homotopy perturbation transform technique to show the efficiency of these techniques. [ABSTRACT FROM AUTHOR]