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: AlgorithmSettings | 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_model" and the Pydantic model associated with the algorithm:

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

BDF#

Module: gemseo.algos.ode.scipy_ode.scipy_ode

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

Pydantic model of the settings for BDF#

from gemseo.settings.ode import BDF_Settings

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

Explicit Runge-Kutta method of order 8

Pydantic model of the settings for DOP853#

from gemseo.settings.ode import DOP853_Settings

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

Adams/BDF method with automatic stiffness detection/switching

Pydantic model of the settings for LSODA#

from gemseo.settings.ode import LSODA_Settings

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

Explicit Runge-Kutta method of order 3(2)

Pydantic model of the settings for RK23#

from gemseo.settings.ode import RK23_Settings

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

Explicit Runge-Kutta method of order 5(4)

Pydantic model of the settings for RK45#

from gemseo.settings.ode import RK45_Settings

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

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

Pydantic model of the settings for Radau#

from gemseo.settings.ode import Radau_Settings

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.