The general family of two-step Runge-Kutta methods introduced by Jackiewicz and Tracogna is investigated in this paper. Conditions for obtaining two-step Runge-Kutta methods which integrate algebraic polynomials exactly are derived. Some simplifying conditions on the parameters of the method, which form the collocation methods within this family of general linear methods, are presented. Two-step Runge-Kutta methods trigonometrically-fitted for ODEs having periodic or oscillatory solution are also considered. The author assumes that the dominant frequency w can be estimated in advance. Based on this assumption the resulting methods depend on the parameter wh, where h is the stepsize. The one-stage case is also investigated.
General Two-Step Runge-Kutta methods based on algebraic and trigonometric polynomials
PATERNOSTER, Beatrice
2001
Abstract
The general family of two-step Runge-Kutta methods introduced by Jackiewicz and Tracogna is investigated in this paper. Conditions for obtaining two-step Runge-Kutta methods which integrate algebraic polynomials exactly are derived. Some simplifying conditions on the parameters of the method, which form the collocation methods within this family of general linear methods, are presented. Two-step Runge-Kutta methods trigonometrically-fitted for ODEs having periodic or oscillatory solution are also considered. The author assumes that the dominant frequency w can be estimated in advance. Based on this assumption the resulting methods depend on the parameter wh, where h is the stepsize. The one-stage case is also investigated.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
