Ordinary differential equations solvers

Warning

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

Note

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

BDF

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.

DOP853

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.

LSODA

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • lband : int | None, optional

    Lower boundary of the bandwidth for the “LSODA” method.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.

  • uband : int | None, optional

    Upper boundary of the bandwidth for the “LSODA” method.

    By default it is set to None.

RK23

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.

RK45

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.

Radau

Module: gemseo.algos.ode.lib_scipy_ode

ODE solver implemented in the SciPy library.

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

Optional parameters

  • atol : float | NDArray[float], optional

    Absolute tolerance.

    By default it is set to 1e-06.

  • first_step : float | None, optional

    Initial step size. If None, let the algorithm choose.

    By default it is set to None.

  • max_step : float, optional

    Maximum allowed step size.

    By default it is set to inf.

  • min_step : float, optional

    Minimum allowed step for the “LSODA” method.

    By default it is set to 0.

  • rtol : float | NDArray[float], optional

    Relative tolerance.

    By default it is set to 0.001.