Here are several variations on the application of Runga-Kutta to a few problems with known solutions.
The details of the code differ and the RK logic has not been entirely standardized and abstracted.
Note the unusual precision available with this compiler.
That compiler does not support independent compilation but it is perfectly adequate for programs of this size, and indeed quite a bit bigger.
Each of these programs include ad-hoc tests to verify agreement with the known solution.
This bends a beam thru a large deflection and duplicates some of these calculations with much more precision.
I want to see if beam bending leads to familiar curves.

A naïve equation solver and matrix inverter.