The application of Rosenbrock-Wanner type methods with stepsize control in differential-algebraic equations

Springer Science and Business Media LLC - Tập 55 - Trang 545-563 - 1989
P. Rentrop1, M. Roche2, G. Steinebach3
1Mathematisches Institut, TU München, München 2, Federal Republic of Germany
2Section de Mathematique, Universite de Geneve, Geneve 24, Switzerland
3FB Mathematik, Universität Kaiserslautern, Kaiserslautern, Federal Republic of Germany

Tóm tắt

Two Rosenbrock-Wanner type methods for the numerical treatment of differential-algebraic equations are presented. Both methods possess a stepsize control and an index-1 monitor. The first method DAE34 is of order (3)4 and uses a full semi-implicit Rosenbrock-Wanner scheme. The second method RKF4DA is derived from the Runge-Kutta-Fehlberg 4(5)-pair, where a semi-implicit Rosenbrock-Wanner method is embedded, in order to solve the nonlinear equations. The performance of both methods is discussed in artificial test problems and in technical applications.

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