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Partitioned Runge-Kutta methods with stiffness detection and stepsize control

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Summary

For the numerical solution of autonomous initial value problems partitioned Runge-Kutta methods are studied, consisting of anA-stable Rosenbrock-Wanner method for the treatment of the stiff components and a customary Runge-Kutta method for the nonstiff part. The equations of condition including the coupling conditions are presented. An automatic stiffness detection and a stepsize control for two different algorithms are developed. The first algorithm PRK4 of order (3)4 possesses an automatic componentwise stiffness detection. The second algorithm RKF4RW treats the whole system as nonstiff or as stiff. RKF4RW is based on the well-known Runge-Kutta-Fehlberg pair of order 4(5). Additionally a ROW method of order (3)4 with anA-stable fourth order approximation is embedded. Usually RKF4RW is the faster algorithm and the system stiffness detection works more reliable than the componentwise stiffness detection in PRK4.

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  1. Fachbereich Mathematik, Universität Kaiserslautern, Erwin Schrödingerstraße, D-6750, Kaiserslautern, Federal Republic of Germany

    Peter Rentrop

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Rentrop, P. Partitioned Runge-Kutta methods with stiffness detection and stepsize control. Numer. Math. 47, 545–564 (1985). https://doi.org/10.1007/BF01389456

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