Simulation of Singular Fourth- Order Partial Differential Equations Using the Fourier Transform Combined With Variational Iteration Method

Abstract

In this paper, we present a comparative study between the modified variational iteration method (MVIM) and a hybrid of Fourier transform and variational iteration method (FTVIM). The study outlines the efficiency and convergence of the two methods. The analysis is illustrated by investigating four singular partial differential equations with variable coefficients. The solution of singular partial differential equations usually needs a coordinate transformation in order to discard the singularity of the partial differential equation. Most often this transformation is not applicable and even does not exist. Therefore in this case the solution for the singular partial differential equation does not exist. In the present study the results of simulation for the singular partial differential equations with variable coefficients using the Fourier transform variational iteration method are compared with the results of simulation using the modified variational iteration method. The comparison shows that the effectiveness and accuracy of Fourier transform variational iteration method is more than that of the modified variational iteration method for the simulation of singular partial differential equations.