Additive Runge-Kutta methods for stiff ordinary differential equations

Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations x' = J(t)x + g(t, x). Pairs of methods, of order p < 4, where one method is semiexplicit and A-stable and the other method is explicit, are obtained. These methods require the LU factorization of one n X n matrix, and p evaluations of g, in each step. It is shown that such methods have a stability property which is similar to a stability property of perturbed linear differential equations. 1. Introduction. In a recent article (2) the authors showed that certain pairs of methods may be used in an additive fashion to solve an initial value problem for a system of n differential equations x' = f(t, x), x(a) = xo, a - t - b,