SIAM Journal on Numerical Analysis, Vol. 26, No. 2 (Apr., 1989), pp. 414-429 (16 pages) Implicit Runge-Kutta-Nyström (RKN) methods are constructed for the integration of second-order differential ...

A contractivity theory of Runge—Kutta methods for stiff nonlinear Volterra functional differential equations (VFDEs) is established, by means of which a family of high order contractive Runge—Kutta ...

I looked up lsode to see what method it uses, and found out that it is another solving method, Livermore solver, and some neural network paper says that it is superior to 5th order Runge-Kutta.