See the full documentation here.
RK-Opt is a collection of MATLAB codes for designing optimized numerical ODE solvers. The main emphasis is on Runge-Kutta methods, but some routines deal with other classes of methods. It is primarily developed and used by the KAUST Numerical Mathematics Group. It includes the following sub-packages:
- polyopt: Find optimal stability polynomials of a given degree and order of accuracy for a specified spectrum.
- 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.
- 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.
A common workflow for designing Runge-Kutta methods is to use polyopt to find an appropriate stability function and then RK-coeff-opt to determine the Runge-Kutta method coefficients.
To run the tests, execute the MATLAB script test.m. This requires a relatively recent
version of MATLAB (tested with R2018a and later) with the following toolboxes.
- MATLAB Optimization Toolbox
- MATLAB Global Optimization Toolbox
- CVX (http://cvxr.com/cvx/)
The code is primarily developed and maintained by David Ketcheson. The following people have also made important contributions to RK-Opt (listed alphabetically):
- Aron Ahmadia: Co-developer of polyopt algorithm and routines.
- Zachary Grant: Extension of order conditions to multistep RK with more than two stages and addition of order conditions for orders 9-11.
- Matteo Parsani: Many improvements to RK-coeff-opt routines and organization.
- Hendrik Ranocha: General improvements and updates, including updating the test routines.