I have started investigating in mostly Runge Kutta and Runge Kutta Nyström methods and there one of the only differences between the methods of the same type is their Butcher tableu. For the most common ones (RK4, RKF45, DOPRI54) they can be found on Wikipedia but otherwise I find it hard to find them. I could always go back the original paper but it can be a bit complicated for a newbie like me to read and understand. For example the Tsistouras 5 integrator. It seems unnecessary if people have to do all that work everytime to get those. Is there any website that has a larger collection of butcher tableus?
The three best sources of Butcher tableaus are, according to me, the reference books
- Numerical Methods for Ordinary Differential Equations, 3rd ed., J.C. Butcher,
- Solving Ordinary Differential Equations I, 2nd ed., Hairer, Norsett and Wanner and
- Solving Ordinary Differential Equations II, 2nd ed., Hairer and Wanner.
You will have to browse through the books but all three of them contain a huge number of tableaus with indications of the "method name" (like Dormand-Prince). Unfortunately, the Butcher book has a very limited index so you'll really need to browse the book.
There is also a comprehensive list on Wikipedia.
The Python package Nodepy has a number of tableaus, and will also generate tableaus for many different families of methods, including some that aren't traditionally viewed as Runge-Kutta methods but can be written that way (e.g., extrapolation methods and deferred correction methods).
Tableaus for many SSP methods can be found at http://sspsite.org; these are usually written in Shu-Osher form rather than Butcher form, since that's also how they are usually implemented.