A New Stiffly Accurate Rosenbrock-Wanner Method for Solving the Incompressible Navier-Stokes Equations

One possibility to solve stiff ODEs like the example of Prothero and Robinson [21] or differential algebraic equations are Runge-Kutta methods (RK methods) [9, 31]. Explicit RK methods may not be a good choice since for getting a stable numerical solution a stepsize restriction should be accepted, i.e. the problem should be solved with very small timesteps. Therefore it might be better to use implicit or linear implicit RK methods, so-called Rosenbrock–Wanner methods. Fully implicit RK methods may be ineffective for solving high dimensional ODEs since they need a high computational effort to solve the huge nonlinear system. Therefore we consider in this note diagonally implicit RK methods (DIRK methods).

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