Additive Runge-Kutta methods for stiff ordinary differential equations

Cooper, G. J.; Sayfy, A.

doi:10.1090/S0025-5718-1983-0679441-1

Additive Runge-Kutta methods for stiff ordinary differential equations
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by G. J. Cooper and A. Sayfy PDF

Math. Comp. 40 (1983), 207-218 Request permission

Abstract:

Certain pairs of Runge-Kutta methods may be used additively to solve a system of n differential equations $x’ = J(t)x + g(t,x)$. Pairs of methods, of order $p \leqslant 4$, where one method is semiexplicit and A-stable and the other method is explicit, are obtained. These methods require the LU factorization of one $n \times n$ 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.

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