Phase-Lag Analysis of Diagonally Implicit Runge-Kutta Methods

This paper concerns an approximation property of diagonally implicit Runge-Kutta methods when they are applied to a system of ordinary differential equations with periodic solutions. In order to characterize the property, phase errors are studied for a Certain class of rational approximations to exp (z) and several Conditions for reducing the phase error are derived. A-acceptability is also considered for the rational approximations in the same class and higher order A-acceptable rational approximations with reduced phase errors are obtained.