ON A PARALLEL DIAGONALLY IMPLICIT RKN METHOD FOR THE NUMERICAL INTEGRATION OF SECOND ORDER DIFFERENTIAL EQUATIONS POSSESSING OSCILLATORY SOLUTIONS - Kolade, Ayodeji David; Imoni, Sunday O.; Lanlege, David I. (FUDMA JOURNAL OF SCIENCES, 2025)
This paper presents a new four stage fourth-order Parallel diagonally implicit Runge-Kutta-Nystrom (RKN) method for the numerical integration of second order initial value problems (IVPs) possessing oscillatory solutions. The stability analysis of the method was also investigated to show that the method can approximate oscillatory systems. Numerical example was presented to show the applicability of the method. The results obtained shows that the method compares favourably in terms of accuracy and convergence with existing methods in current literatures.