A NEW CLASS OF METHODS FOR SOLVING ORDINARY DIFFERENTIAL EQUATIONS

摘要

Almost Runge-Kutta methods are a sub-class of the family of methods known as general linear methods, used for solving ordinary differential equations. They retain many of the properties of traditional Runge-Kutta methods, with some added advantages. The higher stage order enables cheap error estimators to be obtained. For some orders it also means a reduction in the number of internal stages required to obtain that order. We will introduce these methods and present some recent results.