https://www.cambridge.org/core/journals/international-astronomical-union-colloquium/article/an-efficient-integrator-that-uses-gaussradau-spacings/F942BC9121C74C

https://www.cambridge.org/core/journals/international-astronomical-union-colloquium/article/an-efficient-integrator-that-uses-gaussradau-spacings/F942BC9121C74CC2FA296050FC18D824 https://www.cambridge.org/core/journals/international-astron... Here is a heavily used method in astronomy, this involves a higher order polynomial expansion than RK4. This method has been extended a few times, my code uses a variation of it, and I know of several other projects which are also descended from it.