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
Three classes of combined numerical methods for solving the Cauchy problem for a system of differential-algebraic equations with a nontrivial predictor are suggested. For these methods, convergence theorems are proved and the estimates of accuracy solution 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.
system of differential-algebraic equations
scientific article; zbMATH DE number 1467855