Some Runge-Kutta Algorithms with Error Control and Variable Stepsizes for Solving a Class of Differential-Algebraic Equations

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.