ode_expeuler_step

ode_expeuler_step#

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

One-step Exponential Euler method for ODEs with linearized drift.

Examples

>>> def fun(x, t):
...     return -x
>>> x = 1.0
>>> exp_euler_step(fun, x， 0.)

If the variable ( \(x\) ) has units of ( \([X]\) ), then the drift term ( \(\text{drift_fn}(x)\) ) should have units of ( \([X]/[T]\) ), where ( \([T]\) ) is the unit of time.

If the variable ( x ) has units of ( [X] ), then the diffusion term ( text{diffusion_fn}(x) ) should have units of ( [X]/sqrt{[T]} ).

Parameters:

  • f (Callable[[PyTree, float | Quantity, ...], PyTree]) – Drift function f(y, t, *args) used in the exponential update.

  • y (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Current state. Must have a floating dtype.

  • t (Array | ndarray | bool | number | bool | int | float | complex | Quantity) – Current time.

  • *args – Additional positional arguments forwarded to f.

Returns:

The updated state y_{n+1}.

Return type:

PyTree