Experimental dynamics RK4 Butcher tableau typo

Created by: Matematija

Hi,

I was going through your new experimental ODE integrator code and I think I noticed a typo in one of the predefined Butcher tableaus for the RK4 solver. You have:

bt_rk4  = TableauRKExplicit(
                order = (4,),
                a = jnp.array([[0,   0,   0,   0],
                               [1/2, 0,   0,   0],
                               [0,   1/2, 0,   0],
                               [0,   0,   1,   1]], dtype=default_dtype),
                b = jnp.array( [1/6,  1/3,  1/3,  1/6], dtype=default_dtype),
                c = jnp.array( [0, 1/2, 1/2, 1], dtype=default_dtype),
                c_error = None,
                )

while I believe that the correct tableau should be

bt_rk4  = TableauRKExplicit(
                order = (4,),
                a = jnp.array([[0,   0,   0,   0],
                               [1/2, 0,   0,   0],
                               [0,   1/2, 0,   0],
                               [0,   0,   1,   0]], dtype=default_dtype),
                b = jnp.array( [1/6,  1/3,  1/3,  1/6], dtype=default_dtype),
                c = jnp.array( [0, 1/2, 1/2, 1], dtype=default_dtype),
                c_error = None,
                )

(Note the very last matrix element in the a field should be 0, not 1, if I am reading the relevant Wikipedia page correctly.)

It should be a pretty easy thing to fix. :-)