Additive Runge-Kutta methods for stiff ordinary differential equations

Abstract

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 ) x’ = J(t)x + g(t,x) . Pairs of methods, of order p ⩽ 4 p \leqslant 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 × n n \times 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.