On The Simulation of Partial Differential Equations Using the Hybrid of Fourier Transform and Homotopy Perturbation Method

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 closed form solutions obtained from the series solution of recursive sequence forms are obtained. We show that the solutions to the non-homogeneous partial differential equations are valid for the entire range of problem domain. However the validity of the solutions using the previous semi-analytical methods in the entire range of problem domain fails to exist. This is the deficiency of the previous HPMs caused by unsatisfied boundary conditions that is overcome by the new method, the Fourier transform homotopy perturbation method. Moreover, it is shown that solutions approach very rapidly to the exact solutions of the partial differential equations. The effectiveness of the new method for three non-homogenous differential equations with variable coefficients is shown schematically. The very rapid approach to the exact solutions is also shown schematically.