A DIAGONALLY IMPLICIT RUNGE-KUTTA-NYSTROM (RKN) METHOD FOR SOLVING SECOND ORDER ODES ON PARALLEL COMPUTERS - Imoni, Sunday Obomeviekome (FUDMA JOURNAL OF SCIENCES, 2020)
In this paper, diagonally implicit Runge-Kutta-Nystrom (RKN) method of high-order for the numerical solution of second order ordinary differential equations (ODE) possessing oscillatory solutions to be used on parallel computers is constructed. The method has the properties of minimized local truncation error coefficients as well as possessing non-empty interval of periodicity, thus suitable for oscillatory problems. The method was tested with standard test problems from the literature and numerical results compared with the analytical solution to show the advantage of the algorithm