A FOURTH ORDER IMPLICIT SYMMETRIC AND SYMPLECTIC EXPONENTIALLY FITTED RUNGE-KUTTA-NYSTROM METHOD FOR SOLVING OSCILLATORY PROBLEMS

In this paper, we derive an implicit symmetric, symplectic and exponentially fitted Runge-Kutta-Nystrom (ISSEFRKN) method. The new integrator ISSEFRKN2 is of fourth order and integrates exactly differential systems whose solutions can be expressed as linear combinations of functions from the set {exp(lambda t), exp(-lambda t)vertical bar lambda is an element of C}, or equivalently {sin(omega t), cos(omega t)vertical bar lambda = i omega, omega is an element of R}. We analysis the periodicity stability of the derived method ISSEFRKN2. Some the existing implicit RKN methods in the literature are used to compare with ISSEFRKN2 for several oscillatory problems. Numerical results show that the method ISSEFRKN2 possess a more accuracy among them.