Development and Application of an Exponential Method for Integrating Stiff Systems Based on the Classical Runge–Kutta Method

We study numerical methods for solving stiff systems of ordinary differential equations. We propose an exponential computational algorithm which is constructed by using an exponential change of variables based on the classical Runge–Kutta method of the fourth order. Nonlinear problems are used to prove and demonstrate the fourth order of convergence of the new method.