An Implicit Runge-Kutta Method for General Second Order Ordinary Differential Equations
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.
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