4.5.8 pde.solvers.milstein module

Defines an explicit Milstein solver for stochastic differential equations.

MilsteinSolver

Milstein method for stochastic differential equations.

class MilsteinSolver(pde: PDEBase, *, backend: str | pde.backends.base.BackendBase = 'auto', adaptive: bool = False, tolerance: float = 0.0001)[source]

Bases: EulerSolver

Milstein method for stochastic differential equations.

Parameters:

pde (PDEBase) – The partial differential equation that should be solved
backend (str) – The backend used for numerical operations
adaptive (bool) – Whether to use adaptive time stepping
tolerance (float) – Error tolerance for adaptive time stepping

property backend: BackendBase

The backend for this solver.

Type:: BackendBase

property backend_name: str

The name of the backend used for this solver.

Type:: str

classmethod from_name(name: str, pde: PDEBase, **kwargs) → SolverBase

Create a solver object from its registered name.

Solver classes are automatically registered when they inherit from SolverBase. Note that this also requires that the respective python module containing the solver has been loaded before it is attempted to be used.

Parameters:

name (str) – The name of the solver to construct
pde (PDEBase) – The partial differential equation that should be solved
**kwargs – Additional arguments for the constructor of the solver

Returns:

An instance of a subclass of SolverBase

make_stepper(state: TField, dt: float | None = None) → StepperType

Create the executable stepping function produced by this solver.

Parameters:

state (FieldBase) – An example for the state from which the grid and other information can be extracted
dt (float) – Time step used (Uses SolverBase.dt_default if None). This sets the initial time step for adaptive solvers.

Returns:

Function that can be called to advance the state from time t_start to time t_end. The function call signature is (state: numpy.ndarray, t_start: float, t_end: float)