The second-order explicit RKC method

The second-order explicit Runge-Kutta-Chebyshev method(RKC) is an s-stage Runge-Kutta method designed for explicit integration of modestly stiff systems of ordinary differential equations. The method possesses extended real stability interval with a length β proportional to s². Remarkable properties of the RKC method make it possible to select at each size the most efficient stable formula as well as the most efficient step size. By numerical experiments we show that the RKC method is more efficient than Matlab function ode45 to solve the stiff problem. This function is based on a fourth-order explicit RK formula.