ode_ralston3_step

class braintools.quad.ode_ralston3_step(f, y, t, *args, **kwargs)

Ralston’s 3rd-order Runge–Kutta method (optimized RK3).

Butcher tableau

• c = [0, 1/2, 3/4]

• a21 = 1/2; a31 = 0, a32 = 3/4

• b = [2/9, 1/3, 4/9]

Note

This RK3 equals the 3rd-order solution of the Bogacki–Shampine 3(2) pair; see ode_rk23_step/ode_bs32_step for the embedded variant.

param f:

Right-hand side function f(y, t, *args) -> PyTree.

type f:

Callable[[PyTree, float | Quantity, ...], PyTree]

param y:

Current state at time t.

type y:

PyTree

param t:

Current time.

type t:

Array | ndarray | bool | number | bool | int | float | complex | Quantity

type *args:

param *args:

Additional positional arguments forwarded to f.

returns:

The updated state after one Ralston RK3 step.

rtype:

PyTree