Order results for mono-implicit Runge-Kutta methods

Abstract

The mono-implicit Runge-Kutta methods are a subclass of the well-known implicit Runge-Kutta methods and have application in the efficient numerical solution of systems of initial and boundary value ordinary differential equations. Although the efficiency and stability properties of this class of methods have been studied in a number of papers, the specific question of determining the maximum order of an s-stage mono-implicit Runge-Kutta method has not been dealt with. In addition to the complete characterization of some subclasses of these methods having a number of stages s [less than or equal to] 5, a main result of this paper is a proof that the order of an s-stage mono-implicit Runge-Kutta method is at most s + 1.