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Some runge-kutta algorithms with error control and variable stepsizes for solving a class of differentialalgebraic equations

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In this paper, we propose and discuss numerical algorithms for solving a class of nonlinear differential-algebraic equations (DAEs). These algorithms are based on half-explicit Runge-Kutta methods (HERK) that have been studied recently for solving strangeness-free DAEs. The main idea of this work is to use the half-explicit variants of some well-known embedded Runge-Kutta methods such as Runge-Kutta-Fehlberg and Dormand-Prince pairs. Thus, we can estimate local errors and choose suitable stepsizes accordingly to a given tolerance. The cases of unstructured and structured DAEs are investigated and compared. Finally, some numerical experiences are given for illustrating the efficiency of the algorithms. |