A 4(3) pair Runge-Kutta-Nystršm method for periodic initial value problems - Norazak Senu,; Mohamed Suleiman,; Fudziah Ismail,; Mohamed Othman, (Universiti Kebangsaan Malaysia, 2010)
A new embedded 4(3) pair explicit four-stage fourth-order Runge-Kutta-Nyström (RKN) method was developed to integrate second-order differential equations of the form yʺ = f (x, y) where the solution was oscillatory. Presented is a method which has high order dispersion with a ‘small’ principal local truncation error coefficient. The stability analysis of the method derived is also given. Numerical comparisons of this new method with RK4(3) and RKN4(3)D methods show its clear advantage in terms of function evaluations and computation time.