Abstract
This paper studies partitioned linearly implicit Runge-Kutta methods as applied to approximate the smooth solution of a perturbed problem with stepsizes larger than the stiffness parameterε. Conditions are supplied for construction of methods of arbitrary order. The local and global error are analyzed and the limiting caseε → 0 considered yielding a partitioned linearly implicit Runge-Kutta method for differential-algebraic equations of index one. Finally, some numerical experiments demonstrate our theoretical results.
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Strehmel, K., Weiner, R. & Dannehl, I. On error behaviour of partitioned linearly implicit runge-kutta methods for stiff and differential algebraic systems. BIT 30, 358–375 (1990). https://doi.org/10.1007/BF02017354
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DOI: https://doi.org/10.1007/BF02017354