R-Stable Embedded DIRKN Method of Orders 4(3) for Solving Special Second Order IVPs

Abstract

In this paper, we construct embedded diagonally implicit Runge-Kutta- Nystrom (DIRKN) methods of orders 4(3) for the numerical solution of the special second order initial value problems (IVPs) of the differential equation y^¢ = f (x, y) possessing oscillatory solutions. The motivation for this work comes from the fact that not much work seems to have been done on the embedded implicit RKN methods compared to the explicit case. In the present consideration, we derive coefficients of the method with minimized truncation error coefficients and show that it is R-stable.