论文信息 - A new fifth order explicit runge-kutta method with four stages for solving initial value problems in ODSs

A new fifth order explicit runge-kutta method with four stages for solving initial value problems in ODSs

In this paper we present a new four-stage fifth-order explicit method of Runge-Kutta type. The new method is based on a composite derivative strategy and stability and error analyses confirm that the method is stable of fifth order. Two examples are given which illustrate the effectiveness of the method compared to the RK-Nystrom six-stage fifth order method.

David J. Evans | Nazeeruddin Yaacob | D. J. Evans | N. Yaacob

[1] T. E. Hull,et al. Comparing Numerical Methods for Ordinary Differential Equations , 1972 .

[2] J. Lambert. Computational Methods in Ordinary Differential Equations , 1973 .

[3] Lawrence F. Shampine,et al. The Art of Writing a Runge-Kutta Code, Part I , 1977 .

[4] T. E. Hull,et al. A Theoretical Criterion for Comparing Runge–Kutta Formulas , 1978 .

[5] J. Butcher. The numerical analysis of ordinary differential equations: Runge-Kutta and general linear methods , 1987 .

[6] David J. Evans,et al. A fourth order runge-kutta method based on the heronian mean formula , 1995, Int. J. Comput. Math..

[7] Bahrom Sanugi,et al. A new fifth order five-stage runge-kutta method for initial value type problems in odes , 1996, Int. J. Comput. Math..