Runge–Kutta collocation methods for differential-algebraic equations of indices 2 and 3

Stiffly accurate Runge–Kutta collocation methods with explicit first stage are examined. The parameters of these methods are chosen so as to minimize the errors in the solutions to differential-algebraic equations of indices 2 and 3. This construction results in methods for solving such equations that are superior to the available Runge–Kutta methods.