in this paper, the solution of the evolutionaryfourth-order in space, sivashinsky equation is obtained by meansof homotopy perturbation method (textbf{hpm}). the results revealthat the method is very effective, convenient  and quite accurateto systems of nonlinear partial differential equations.

In this paper, we propose a new approach to solve the unsteady gas equation. We apply the Modified Laplace decomposition method (MLDM) coupled with Pade ́ approximation to compute a series solution of unsteady flow of gas through a porous medium. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. The nonlinear terms can be easil...

here, a new method called aboodh transform homotopy perturbation method(athpm) is used to solve nonlinear partial dierential equations, we presenta reliable combination of homotopy perturbation method and aboodh transformto investigate some nonlinear partial dierential equations. the nonlinearterms can be handled by the use of homotopy perturbation method. the resultsshow the eciency of this...

This paper is devoted to introduce analytic solutions by Differential Transform Method-Pade approximants with theoretical study for the problem of the hydromagnetic flow due to a permeable stretching surface embedded in a porous medium in the presence of transverse magnetic field. The governing momentum equation which is a nonlinear partial differential equation is reduced into a nonlinear ordi...

in this paper, we conduct a comparative study between the homotopy perturbation method (hpm) and adomian’s decomposition method (adm) for analytic treatment of nonlinear volterra integral equations, and we show that the hpm with a specific convex homotopy is equivalent to the adm for these type of equations.

In this paper, Elzaki Homotopy Perturbation Method is employed for solving linear and nonlinear differential equations with a variable coffecient. This method is a combination of Elzaki transform and Homotopy Perturbation Method. The aim of using Elzaki transform is to overcome the deficiencies that mainly caused by unsatised conditions in some semi-analytical methods such as Homotopy Perturbat...

solitons are ubiquitous and exist in almost every area from sky to bottom. for solitons to appear, the relevant equation of motion must be nonlinear. in the present study, we deal with the korteweg-devries (kdv), modi ed korteweg-de vries (mkdv) and regularised longwave (rlw) equations using homotopy perturbation method (hpm). the algorithm makes use of the hpm to determine the initial expansio...

We investigate convergence of the rational-trigonometric-polynomial interpolation that performs convergence acceleration of the classical trigonometric interpolation by sequential application of polynomial and rational correction functions. Unknown parameters of the rational corrections are determined along the ideas of the Fourier-Pade approximations. The resultant interpolation we call as Fou...

The Extended Euclidean algorithm for matrix Pade approximants is applied to compute matrix Pade approximants in rectangular full packed format (RFP) if the coefficient matrices of the input matrix polynomial are triangular. The procedure given by Gustavson et al for packing a triangular matrix in rectangular full packed format is applied to pack sequence of lower triangular matrices of a matrix...