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

Implicit ordinary differential equations, differential-algebraic equations (34A09) Stability and convergence of numerical methods for ordinary differential equations (65L20) Numerical methods for initial value problems involving ordinary differential equations (65L05) Multistep, Runge-Kutta and extrapolation methods for ordinary differential equations (65L06) Error bounds for numerical methods for ordinary differential equations (65L70) Numerical methods for differential-algebraic equations (65L80) Mesh generation, refinement, and adaptive methods for ordinary differential equations (65L50)