qmat.qcoeff.collocation

Submodule to generate Q matrices based on Collocation

Examples

>>> from qmat.qcoeff.collocation import Collocation
>>> coll = Collocation(nNodes=4, nodeType="LEGENDRE", quadType="RADAU-RIGHT")
>>> nodes, weights, Q = coll.genCoeffs()
>>> S = coll.S

Classes

Base class to generate \(Q\)-coefficients for a Collocation method.

Module Contents

class Collocation(nNodes, nodeType, quadType, tLeft=0, tRight=1)[source]

Inheritance diagram of qmat.qcoeff.collocation.Collocation

Base class to generate \(Q\)-coefficients for a Collocation method.

Parameters:

nNodes (int) – Number of collocation nodes.
nodeType (str) – Type of node distributions, see qmat.nodes for possible choices.
quadType (str) – Quadrature type, see qmat.nodes for possible choices.
tLeft (float, optional) – Left boundary for the nodes. The default is 0.
tRight (float, optional) – Right boundary for the nodes. The default is 1.

aliases = ['coll']

DEFAULT_PARAMS: Defaults parameters for getInstance

approx

property nodes: numpy.ndarray: Nodes \(\tau\) (\(c\) coefficients in Butcher table)

property Q: numpy.ndarray: \(Q\) coefficients (\(A\) Butcher table)

property weights: numpy.ndarray: Weights \(\omega\) (\(b\) coefficients in Butcher table)

property S: numpy.ndarray: Quadrature matrix in node to node (N2N)

property hCoeffs: numpy.ndarray: \(h\) interpolation coefficients for the right boundary

property order: int: Global convergence order of the method