BackwardsEulerStep

Defaults

algorithm="backwards_euler" performs a single-stage, order-1 backward-Euler update under fixed-step control; the method carries no embedded error estimate, so adaptive control is unavailable. Each step solves the implicit stage equation with the shared Newton–Krylov defaults listed in Default settings.

class cubie.integrators.BackwardsEulerStep(precision: type[float16] | type[float32] | type[float64] | dtype[float16] | dtype[float32] | dtype[float64], n_states: int, dxdt_fn: Callable | None = None, observables_fn: Callable | None = None, drivers_fn: Callable | None = None, get_solver_helper_fn: Callable | None = None, **kwargs)

Bases: ODEImplicitStep

Backward Euler step solved with matrix-free Newton–Krylov.

__init__(precision: type[float16] | type[float32] | type[float64] | dtype[float16] | dtype[float32] | dtype[float64], n_states: int, dxdt_fn: Callable | None = None, observables_fn: Callable | None = None, drivers_fn: Callable | None = None, get_solver_helper_fn: Callable | None = None, **kwargs) → None

Initialise the backward Euler step configuration.

Parameters:

• precision – Precision applied to device buffers.

• n_states – Number of state entries advanced per step.

• dxdt_fn – Device function for evaluating f(t, y) right-hand side.

• observables_fn – Device function computing system observables.

• drivers_fn – Optional device function evaluating drivers at arbitrary times.

• get_solver_helper_fn – Callable returning device helpers used by the nonlinear solver.

• **kwargs – Optional parameters passed to config classes. See BackwardsEulerStepConfig, ImplicitStepConfig, and solver config classes for available parameters. None values are ignored.

build_step(dxdt_fn: Callable, observables_fn: Callable, drivers_fn: Callable | None, solver_function: Callable, numba_precision: type, n: int, n_drivers: int) → StepCache

Build the device function for a backward Euler step.

Parameters:

• dxdt_fn – Device function for evaluating f(t, y).

• observables_fn – Device function for computing observables.

• drivers_fn – Optional device function for evaluating drivers at time t.

• solver_function – Device function for the Newton-Krylov nonlinear solver.

• numba_precision – Numba precision corresponding to the configured precision.

• n – Dimension of the state vector.

• n_drivers – Number of driver signals provided to the system.

Returns:

Container holding the compiled step function and solver.

Return type:

StepCache

classmethod family_defaults(tableau=None) → AlgorithmDefaults

Return the backward Euler defaults.

has_error_estimate = False

property is_multistage: bool

Return False because backward Euler is a single-stage method.

property order: int

Return the classical order of the backward Euler method.

register_buffers() → None

Register buffers with buffer_registry.

property threads_per_step: int

Return the number of threads used per step.