The solution of nonlinear parabolic equation using variational iteration method

Variational iteration method is a semi analytic solution used to solve the parabolic differential equation both of homogen or nonhomogen. In the process of determining an approximation solution, this method did not use a linearization and a small pertubation. In this paper, the variational iteration method is implemented in the parabolic differential equation in the form of ut = uxx + f(u) + g(x, t) with appropriate intial condition. Furthermore, some examples of special parabolic differential equations are given to test the reliability and convergence of the method. Based on the result of study shows that the variational iteration method is able to solve the parabolic differential equation with a good accuration.

A Compact Difference Scheme for Solving Fractional Neutral Parabolic Differential Equation with Proportional Delay

A linearized compact finite difference scheme is constructed for solving the fractional neutral parabolic differential equation with proportional delay. By the energy method, the unconditional stability of the scheme is proved, and the convergence order of the scheme is proved to be O(τ2-α+h4). A numerical test is also conducted to validate the accuracy and efficiency of the numerical algorithm.