In this study, we find the exact solution of certain partial differential equations (PDE) by proposing and using the Homo-Separation of Variables method. This novel analytical method is a combination of the homotopy perturbation method (HPM) with the separation of variables method. The exact solutions are constructed by choosing an appropriate initial approximation in addition to only one term ...

This paper targets to investigate the numerical solution of -th order fuzzy differential equations with fuzzy environment using Homotopy Perturbation Method (HPM). Triangular fuzzy convex normalized sets are used for the fuzzy parameter and variables. Obtained results are compared with the existing solution depicted in term of plots to show the efficiency of the applied method.

In this paper, a comparison among the hybrid of Fourier Transform and AdomianDecomposition Method (FTADM) and Homotopy Perturbation Method (HPM) is investigated.The linear and non-linear Newell-Whitehead-Segel (NWS) equations are solved and the results arecompared with the exact solution. The comparison reveals that for the same number of componentsof recursive sequences, the error of FTADM is ...

In this article New Iterative Method (NIM) is tested upon time fractional coupled ITO system. The results obtained by the proposed method are compared with that of Homotopy Perturbation (HPM). It shown accurate for strongly nonlinear system PDEs.

We apply a relatively new technique which is called the homotopy perturbation method (HPM) for solving linear and nonlinear partial differential equations. The suggested algorithm is quite efficient and is practically well suited for use in these problems. The proposed iterative scheme finds the solution without any discretization, linearization or restrictive assumptions. Several examples are ...

Generalized approximation technique for a solution of one-dimensional steady state heat transfer problem in a slab made of a material with temperature dependent thermal conductivity, is developed. The results obtained by the generalized approximation method (GAM) are compared with those studied via homotopy perturbation method (HPM). For this problem, the results obtained by the GAM are more ac...

In this work, the homotopy perturbation method (HPM) is used to solve initial valueproblems of first order with various types discontinuities. The numerical results obtained (arecompared) using traditional HPM, and integral equation nth thesolution Simpson Trapezoidal Rules demonstrate that are extremely accurate when compared exact solution. maximumabsolute error, ‖ . , maximum relative residu...

In this paper, we give an analytical approximate solution for non-linear quadratic optimal control problems and optimal control of linear systems using the homotopy perturbation method (HPM). Applying the HPM, the non-linear two-point boundary-value problem (TPBVP) and linear systems, derived from the Pontryagin’s maximum principle, are transformed into a sequence of linear time-invariant TPBVP...

In this article, we presented a new approach deduced from He’s homotopy perturbation method (HPM) to obtain exact and/or approximate analytical solutions of Emden–Fowler type equations. The results reveal that the proposed algorithm is very effective and in most cases yield exact solutions in the first approximation. Some examples are given to illustrate the new approach.