Fourth-Order Time Stepping for Stiff PDEs via Integrating Factor

The usual technique of numerical solutions of ordinary differential equations (ODE) consists of several fragments that were formed during a long period of time in order to find solutions for the equations. The method like Runge-Kutta that was well established is still being used as the basis of many efficient codes. However, the stiff type problems seem cannot be solved efficiently via some of these methods. This study overcomes such problems via the exponential method. In the first part of this paper, the exponential time differencing Runge-Kutta 4 method (ETDRK4) is used to solve the diagonal example of Kuramoto-Sivashinsky (K-S) equation. The second part is to solve Korteweg-de Vries (KdV) equation with Fourier transformation, and together with implementation of integrating factor method.