imex_cnab_step

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imex_cnab_step#

class braintools.quad.imex_cnab_step(f_exp, f_imp, y, y_prev, t, *args, max_iter=2, **kwargs)#

CNAB (Crank–Nicolson / Adams–Bashforth) IMEX step (second order).

Advances using explicit AB2 for the nonstiff part and trapezoidal rule for the stiff part:

``y_{n+1} = y_n + dt * [ 3/2 f_exp(y_n, t_n) - 1/2 f_exp(y_{n-1}, t_{n-1}) ]

  • dt/2 * [ f_imp(y_{n+1}, t_{n+1}) + f_imp(y_n, t_n) ]``

Parameters:

  • f_exp (Callable[[PyTree, Array | ndarray | bool | number | bool | int | float | complex | Quantity, Any], PyTree]) – Explicit and implicit functions.

  • f_imp (Callable[[PyTree, Array | ndarray | bool | number | bool | int | float | complex | Quantity, Any], PyTree]) – Explicit and implicit functions.

  • y (PyTree) – Current state at time t.

  • y_prev (PyTree) – Previous state at time t - dt.

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

  • *args – Extra arguments forwarded to f_exp and f_imp.

  • max_iter (int) – Fixed‑point iterations for the implicit corrector.

Returns:

The updated state y_{n+1}.

Return type:

PyTree

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