Generalized Runge-Kutta Processes for Stiff Initial-value Problems†

Abstract

We consider the numerical solution of initial value problems y' = f(t,y), y(0) = y0 which are stiff. By considering a suitably transformed problem, a class of explicit A-stable and stiffly A-stable methods is developed. It is shown that these methods integrate exactly any particular integral of the initial value problem y'= Ay+p(t), p(t) a polynomial of degree restricted only by the order of the method, and A a real nonsingular square matrix. It is also shown through numerical examples that the class of methods can be applied effectively to non-linear problems.