choreo.segm.multiprec_tables.ComputeImplicitRKTable#

ComputeImplicitRKTable(n=2, dps=60, method='Gauss', nodes=None)[source]#

Computes a choreo.segm.ODE.ImplicitRKTable

The computation is performed at a user-defined precision using mpmath to ensure that the result does not suffer from precision loss, even at relatively high orders.

Available choices for method are:

  • "Gauss"

  • "Radau_IA", "Radau_IIA", "Radau_IB" and "Radau_IIB"

  • "Lobatto_IIIA", "Lobatto_IIIB", "Lobatto_IIIC", "Lobatto_IIIC*", "Lobatto_IIID" and "Lobatto_IIIS"

  • "Cheb_I" and "Cheb_II"

  • "ClenshawCurtis"

  • "NewtonCotesOpen" and "NewtonCotesClosed"

Alternatively, the user can supply an array of node values between 0. and 1.. The result is then the associated collocation method. Cf Theorem 7.7 of [1] for more details.

Cited:

Example

>>> import choreo
>>> Gauss = choreo.segm.multiprec_tables.ComputeImplicitRKTable(n=2, dps=60, method="Gauss")
>>> Gauss
ImplicitRKTable object of order 2
>>> Gauss.a_table
array([[ 0.25      , -0.03867513],
    [ 0.53867513,  0.25      ]])
>>> Gauss.b_table
array([0.5, 0.5])
>>> Gauss.c_table
array([0.21132487, 0.78867513])
Parameters:

  • n (int, optional) – Order of the method. By default 2.

  • dps (int, optional) –

    Context precision in mpmath. See Contexts for more info. By default 30.

  • method (str, optional) – Name of the method, by default "Gauss".

  • nodes (numpy.ndarray | mpmath:mpmath.matrix | None, optional) – Array of integration node values. By default, None.

Returns:

The resulting nodes and weights of the quadrature.

Return type:

choreo.segm.quad.QuadTable