runge-kutta-4 | The fourth order Runge-Kutta integration method | SMS library

v2 = v2 + RK4(v+v2,h/2,cant_ec) is wrong, it should be v2 = RK4(v2,h/2,cant_ec), as the result of RK4 is the next point, not the update to the next point. As the error calculation is thus wrong, the step size gets reduced indefinitely. After some 50 reductions, the RK4 step will no longer advance the state, the increment being too small.

It will lead to problems if you have a fixed step number with a variable step size.

The inner loop does not make any sense whatsoever. The overall effect is that after each step size reduction i gets incremented by one. So theoretically, if n<50 the program should terminate, but with a final state very close to the initial state.

The local error should be compared to tol*h, so that the global error becomes proportional to tol.

There should also be an instruction that increases h if the local error becomes too small.

See How to perform adaptive step size using Runge-Kutta fourth order (Matlab)? for another example of using RK4 with step-size control by double steps.