Stability of the Rosenbrock methods for the neutral delay differential-algebraic equations

This paper develops the Rosenbrock methods for the neutral delay differential-algebraic equations (NDDAEs) and proves that the Rosenbrock methods equipped with suitable interpolation are GP-stable under proper assumption for the linear neutral delay differential-algebraic equations with constant coefficients. Furthermore, the GP-stability of the Runge-Kutta methods is also considered. The discussions are supported by the numerical experiments.