AN IMPLICIT RUNGE-KUTTA METHOD FOR GENERAL SECOND ORDER ORDINARY DIFFERENTIAL EQUATIONS

Abstract. This paper focuses on the derivation of a fully implicit Sixth order Runge-kutta type method with error estimation formula for the solution of general second order ordinary differential equations (ODEs). We define a transformation on the set of coefficients (Butcher coefficients Tableau) for first order differential equations to generate a new coefficient tableau for direct solution of second order ODEs. The scheme is simple, A-stable, highly efficient and has low implementation cost. Some problems are used as experimental examples