Ordinary differential equations solvers

Warning

Some capabilities may require the installation of GEMSEO with all its features and some others may depend on plugins.

Warning

All the features of the wrapped libraries may not be exposed through GEMSEO.

Note

The algorithm settings can be passed to a function of the form

function(..., settings_model: Base | None = None, **settings: Any)

either one by one:

function(..., setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)

or using the argument name "settings" and the Pydantic model associated with the algorithm:

settings = AlgorithmSettings(setting_name_1=setting_name_1, setting_name_2=setting_name_2, ...)
function(..., settings_model=settings)

BDF

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import BDF_Settings

Implicit multi-step variable-order (1 to 5) method based on a backward differentiation formula for the derivative approximation

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.BDF.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• jac_sparsity : typing.Optional[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]]], optional

  Sparsity structure of the Jacobian matrix.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.

DOP853

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import DOP853_Settings

Explicit Runge-Kutta method of order 8

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.DOP853.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.

LSODA

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import LSODA_Settings

Adams/BDF method with automatic stiffness detection/switching

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.LSODA.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• lband : typing.Optional[int], optional

  The lower boundary of the bandwidth of the Jacobian.

  The SciPy documentation does not mention what happens if None.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• min_step : <class 'int'>, optional

  Minimum allowed step size.

  By default it is set to 0.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.

• uband : typing.Optional[int], optional

  The upper boundary of the bandwidth of the Jacobian.

  The SciPy documentation does not mention what happens if None.

  By default it is set to None.

RK23

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import RK23_Settings

Explicit Runge-Kutta method of order 3(2)

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.RK23.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.

RK45

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import RK45_Settings

Explicit Runge-Kutta method of order 5(4)

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.RK45.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.

Radau

Module: gemseo.algos.ode.scipy_ode.scipy_ode

from gemseo.settings.ode import Radau_Settings

Implicit Runge-Kutta method of the Radau IIA type of order 5

More details about the algorithm and its settings on https://docs.scipy.org/doc/scipy/reference/generated/scipy.integrate.Radau.html.

Optional settings

• atol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The absolute tolerance.

  By default it is set to 1e-06.

• first_step : typing.Optional[typing.Annotated[float, Gt(gt=0)]], optional

  The initial step size.

  If None, let the algorithm choose.

  By default it is set to None.

• jac_sparsity : typing.Optional[gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[float]]], optional

  Sparsity structure of the Jacobian matrix.

  By default it is set to None.

• max_step : <class 'float'>, optional

  The maximum allowed step size.

  By default it is set to inf.

• rtol : typing.Union[typing.Annotated[float, Gt(gt=0)], gemseo.utils.pydantic_ndarray._NDArrayPydantic[typing.Any, numpy.dtype[typing.Annotated[float, Gt(gt=0)]]]], optional

  The relative tolerance.

  By default it is set to 0.001.