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Mathematics of Computation

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Additive Runge-Kutta methods for stiff ordinary differential equations

Authors: G. J. Cooper and A. Sayfy
Journal: Math. Comp. 40 (1983), 207-218
MSC: Primary 65L05
MathSciNet review: 679441
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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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Article copyright: © Copyright 1983 American Mathematical Society