Implicit Runge-Kutta methods for transferable differential-algebraic equations
The numerical solution of transferable differential-algebraic equations (DAE's) by implicit Runge-Kutta methods (IRK) is studied. If the matrix of coefficients of an IRK is non-singular then the arising systems of nonlinear equations are uniquely solvable. These methods are proved to be stable if an additional contractivity condition is satisfied. For transferable DAE's with smooth solution we get convergence of order $min(k_E,k_I + 1)$, where $k_E$ is the classical order of the IRK and $k_I$ is the stage order. For transferable DAE's with generalized solution convergence of order 1 is ensured, provided that $k_E ≥ 1$.