Repeated occurrence of Runge-Kutta-Nyström issues concerning their accuracy #1938
Description
So far there where a few issues with the Runge-Kutta-Nyström solvers concerning their accuracy:
- SecondOrderODEProblem gives wrong result DifferentialEquations.jl#726
- StackOverflow: Second order ODE giving wrong results DifferentialEquations.jl#751
- DPRKNs diverge on an example #1030
- DPRKN6 gives substantially different answer on a second order ODE than Tsit5 #1372
All Nyström solvers used, in these issues, are designed for 2nd order ODEs which are not dependent on the first derivative.
However most of the issues feature this type of 2nd order ODE. The lack of accuracy may just boil down to the solvers not being designed for theses types of problems. Any ideas on how to prevent these issues in the future?