THE FOURTH ORDER RUNGE-KUTTA EXPONENTIAL TIME DIFFERENCE METHOD FOR THE ALLEN-CAHN EQUATION

In this paper we present a numerical method for solving the Allen-Cahn equation with a corresponding boundary condition. The Allen-Cahn equation is discretized by the Chebyshev spectral method in space. We use the Fourth Order Runge-Kutta Exponential Time Difference method with Fourier's transformation for its diagonalization in time. The numerical results of solution of the Allen-Cahn equation are obtained by using Matlab code.