order results for algebraically stable mono-implicit runge-kutta methods

摘要

It is well known that mono-implicit Runge-Kutta methods have been applied in the efficient numerical solution of initial or boundary value problems of ordinary differential equations. Burrage (1994) has shown that the order of an s-stage mono- implicit Runge-Kutta method is at most S + 1 and the stage order is at most 3. In this paper, it is shown that the order of an s-stage mono-implicit Runge-Kutta Method being algebraically stable is at most min (s, 4), and the stage order together With the optimal B-convergence order is at most min s, 2), where S = {~s+1 if s = 1,2, _s if s ≥ 3.