In the present work, a hybrid of Fourier transform and homotopy perturbation method is developed for solving the non-homogeneous partial differential equations with variable coefficients. The Fourier transform is employed with combination of homotopy perturbation method (HPM), the so called Fourier transform homotopy perturbation method (FTHPM) to solve the partial differential equations. The c...

In this article, we present some approximate analytical solutions to the general perturbed KdV-Burgers equation with nonlinear terms of any order by applying the homotopy analysis method (HAM). While compared with the Adomain decomposition method (ADM) and the homotopy perturbation method (HPM), the HAM contains the auxiliary convergence-control parameter ~ and the control function H(x, t), whi...

in this paper, the variational homotopy perturbation method (vhpm) and its convergence is adopted for thezakharove-kuznetsov equations (zk-equations). the aim of this paper is to present an efficient and reliabletreatment of the vhpm for the nonlinear partial differential equations and show that this method is convergent.the convergence of the applied method is approved using the method of majo...

In this work, the Blasius equation is studied. Homotopy perturbation method (HPM) and homotopy analysis method (HAM) are applied to obtain its solution. Comparison with variational iteration method (VIM) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. The outcome shows the success of (HPM) and (HAM) for solving nonlinear pro...

We introduce and discuss the Homotopy perturbation method, the Adomian decomposition method and the variational iteration method for solving the stefan problem with kinetics. Then, we give an example of the stefan problem with  kinetics and solve it by these methods.

In this paper, we present an efficient numerical algorithm for solving fuzzy systems of linear equations based on homotopy perturbation method. The method is discussed in detail and illustrated by solving some numerical examples.

in this work, the blasius equation is studied. homotopy perturbation method (hpm) and homotopy analysis method (ham) are applied to obtain its solution. comparison with variational iteration method (vim) is made to highlight the significant features of employed methods and their capability of handling nonlinear problems. the outcome shows the success of (hpm) and (ham) for solving nonlinear pro...

An efficient and accurate analytical solution is provided using the homotopy-Pade technique for the nonlinear vibration of parametrically excited cantilever beams. The model is based on the Euler-Bernoulli assumption and includes third order nonlinear terms arisen from the inertial and curvature nonlinearities. The Galerkin’s method is used to convert the equation of motion to a nonlinear ordin...

although homotopy-based methods, namely homotopy analysis method andhomotopy perturbation method, have largely been used to solve functionalequations, there are still serious questions on the convergence issue of thesemethods. some authors have tried to prove convergence of these methods, butthe researchers in this article indicate that some of those discussions are faulty.here, after criticizi...