`scipy.integrate._bvp:collocation_fun`

source: /scipy/integrate/_bvp.py :277

Signature

def collocation_fun ( fun , y , p , x , h )

Summary

Evaluate collocation residuals.

Extended Summary

This function lies in the core of the method. The solution is sought as a cubic C1 continuous spline with derivatives matching the ODE rhs at given nodes x. Collocation conditions are formed from the equality of the spline derivatives and rhs of the ODE system in the middle points between nodes.

Such method is classified to Lobbato IIIA family in ODE literature. Refer to ^[1] for the formula and some discussion.

Returns

col_res : ndarray, shape (n, m - 1): Collocation residuals at the middle points of the mesh intervals.
y_middle : ndarray, shape (n, m - 1): Values of the cubic spline evaluated at the middle points of the mesh intervals.
f : ndarray, shape (n, m): RHS of the ODE system evaluated at the mesh nodes.
f_middle : ndarray, shape (n, m - 1): RHS of the ODE system evaluated at the middle points of the mesh intervals (and using y_middle).

Aliases

scipy.integrate._bvp.collocation_fun