Numerical solution of the Cauchy problem for a system of differential-algebraic equations with the use of implicit Runge-Kutta methods with a nontrivial predictor

Computational Mathematics and Mathematical Physics, 38(1) (1998), 64-80

Three classes of combined numerical methods for solving the Cauchy problem for a system of differential-algebraic equations with a nontrivial predictor are suggested; the methods are based on implicit Runge–Kutta formulas. For these combined methods, convergence theorems are proved and estimates of solution accuracy are obtained. Numerical methods with fixed and automatically selected integration steps are considered. Among the mentioned classes of methods, the class requiring the least computational time is found. The obtained results are illustrated by numerical examples.