keywords: Numerical analysis, ordinary differential equations, initial value problems
The derivation of implicit Runge-Kutta-Nystrom (RKN) scheme with continuous coefficients for the direct approximation of special second Order ordinary initial value problems(IVPs) using the theory of s-stage Runge-Kutta (RK) for first order ordinary differential equations is presented. The study provides the use of both collocation and interpolation procedure to obtain the scheme. Based on a homogeneous test model, the stability and error analysis of the scheme is also investigated. The continuous formulation of the integrator will enable us to evaluate at some grid and off grid points in the integration interval. The advantage of the continuous scheme as against the discrete schemes for the direct integration of the second order special IVP includes the fact that multiple discrete schemes can be obtained. Numerical examples have been included to demonstrate the accuracy of the scheme.