See the full documentation here.

RK-opt is a collection of MATLAB code for designing optimized Runge-Kutta methods. It is primarily developed and used by the KAUST Numerical Mathematics Group. It includes the following sub-packages:

• RK-coeff-opt: Find optimal Runge-Kutta method coefficients, for a prescribed order of accuracy and number of stages.
• am_rad-opt: Find stability functions with optimal radius of absolute monotonicity. Includes capabilities for both multistep and multistage methods.
• polyopt: Find optimal stability polynomials of a given degree and order of accuracy for a specified spectrum.
• RKtools: A collection of routines for analyzing or computing various properties of Runge-Kutta methods. For a much more extensive package along these lines, see NodePy.

The following people have contributed code to RK-opt (listed alphabetically):

• Aron Ahmadia: polyopt routines
• David Ketcheson: Principal author and maintainer
• Matteo Parsani: RK-coeff-opt routines and organization
• Zachary Grant: Extension of order conditions to multistep RK with more than two stages and addition of order conditions for orders 9-11.