Order conditions for the stochastic Runge–Kutta methods assuring weak convergence with order two are calculated by applying the colored rooted tree analysis due to the author. Further, some ...

Inmaculada Higueras, Representations of Runge-Kutta Methods and Strong Stability Preserving Methods, SIAM Journal on Numerical Analysis, Vol. 43, No. 3 (2006), pp. 924-948 ...

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.