Explicit Runge-Kutta (-Nystroem) Methods with Reduced Phase Errors for Computing Oscillating Solutions

摘要

Explicit Runge-Kutta (-Nystroem) RK(N) methods for the integration of first (and second) order differential equations having an oscillatory solution are constructed. Phase errors (or dispersion) of the dominant components in the numerical oscillations when these methods are applied to a linear, homogeneous test model are discussed. Several RK(N) methods which are dispersive of orders up to 10, whereas the (algebric) order of accuracy is only 2 or 3, are constructed. Application of these methods to semidiscretized hyperbolic equations and to equations describing free and weakly forced oscillations reveals that the phase errors can be significantly reduced.