autopdex.dae.BackwardDiffFormula

class autopdex.dae.BackwardDiffFormula(num_steps)

Backward differentiation formula (BDF).

Parameters:

num_steps (int) – Number of previous steps (1 to 6).

Number of stages: 1, implicit.

__init__(num_steps)

Initializes the time integrator.

Parameters:

• name (str) – The name of the method.

• value_and_derivatives (callable) – Function to compute state values and their derivatives.

• update (callable) – Function that updates the state based on stage results.

• stage_list (ndarray) – Array containing the indices or order of stages.

• stage_types (tuple) – Tuple indicating the type of each stage (‘explicit’ or ‘implicit’).

• stage_positions (ndarray) – Array of stage positions (e.g., Butcher nodes).

• num_steps (int) – Number of previous steps (for multi-step methods).

• num_derivs (int) – Highest derivative order that is supported.

• num_stages (int) – Number of stages (e.g., in Runge–Kutta methods).

Methods

__delattr__(name, /)	Implement delattr(self, name).
__dir__()	Default dir() implementation.
__eq__(value, /)	Return self==value.
__format__(format_spec, /)	Default object formatter.
__ge__(value, /)	Return self>=value.
__getattribute__(name, /)	Return getattr(self, name).
__getstate__()	Helper for pickle.
__gt__(value, /)	Return self>value.
__hash__()	Return hash(self).
__init_subclass__	This method is called when a class is subclassed.
__le__(value, /)	Return self<=value.
__lt__(value, /)	Return self<value.
__ne__(value, /)	Return self!=value.
__new__(**kwargs)
__reduce__()	Helper for pickle.
__reduce_ex__(protocol, /)	Helper for pickle.
__repr__()	Return repr(self).
__setattr__(name, value, /)	Implement setattr(self, name, value).
__sizeof__()	Size of object in memory, in bytes.
__str__()	Return str(self).
__subclasshook__	Abstract classes can override this to customize issubclass().
_error_estimate(q, q_n, q_t_n, dt)	Computes an error estimate for the integrator.
_rule(q, q_n, q_t_n, dt)	Computes the function value and temporal derivative for an integrator, e.g.
_update(q_stages, q_n, q_t_n, dt)	Updating rule after solving the step.

Attributes

__abstractmethods__
__annotations__
__dict__
__doc__
__module__
__slots__
__weakref__	list of weak references to the object
_abc_impl