• APPLICATION OF HOMOTOPY PERTURBATION TRANSFORM METHOD FOR SOLVING HEAT LIKE AND WAVE LIKE EQUATIONS WITH VARIABLE COEFFICIENTS

V. G. Gupta, Sumit Gupta*

Abstract


In this paper, we apply homotopy perturbation transform method (HPTM) for solving various heat-like and wave-like equations. This method is the combined form of homotopy perturbation method and Laplace transform method. The nonlinear terms can be easily obtained by the use of He's polynomials. HPTM presents an accurate methodology to solve nonhomogeneous partial differential equations of variable coefficients. The aim of using the Laplace transform is to overcome the deficiency that is mainly caused by unsatisfied conditions in the other semi analytical methods such as Homotopy perturbation method (HPM), Variational iteration method (VIM) and Adomain decomposition method (ADM). The approximate solutions obtained by means of HPTM in a wide range of problem's domain were compared with those results obtained from the actual solution. The fact that proposed technique solves nonlinear problems can be considered as a clear advantage of this algorithm over the decomposition method.

Keywords


Homotopy perturbation method, Laplace transform method, Parabolic-like equations, Hyperbolic-like equations, He's polynomials.

Full Text:

PDF


Creative Commons License
This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.
© 2010-2020 International Journal of Mathematical Archive (IJMA)
Copyright Agreement & Authorship Responsibility
Web Counter