RKCheck

RKcheck is a Java-based application designed to verify the order of Runge-Kutta methods. This method is described using an XML file with the Butcher-array structure. The application computes the order conditions and checks if the defined method in the XML file follows these conditions. If the method has coefficients for error estimation, the order of the error estimation is also verified.

The XML file contains a specific structure to describe the method, such as the classical Runge-Kutta. The Butcher-array corresponding to this method is shown in a human-readable format. If the coefficients in the XML file are all exact, the computation is also exact with no approximation at all. However, if the coefficients' exact expression is unknown, they can be entered as real values with arbitrary precision using the ...< /real> elements.

To use approximation in the final check with inexact coefficients, the user must use the -tolerance command-line switch. If all the coefficients are exact, the computation is also exact, and there is no need for approximation. The exact coefficients are integers, rational numbers, and quadratic surds.

The application comes with a default manifest file that declares org.spaceroots.rkcheck.CheckOrderConditions as the main class of the jar file. Users can also use another main class, org.spaceroots.rkcheck.ComputeOrderConditions, which does not read any XML method file. Instead, it writes all the order conditions up to a user-defined order in LaTeX format or in Maxima format.

The application has specific requirements, such as ant and junit, necessary only for rerunning tests. Overall, RKcheck is a helpful tool recommended for anyone working with Runge-Kutta methods.