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In fact, one can show that the order of a collocation method corresponds to the order of the quadrature rule that one would get using the collocation points as weights.
== Orthogonal collocation method ==
'''Orthogonal collocation''' is a method for the [[Numerical partial differential equations|numerical solution of partial differential equations]]. It uses [[Collocation method|collocation]] at the zeros of some [[orthogonal polynomials]] to transform the [[partial differential equation]] (PDE) to a set of [[Ordinary differential equation|ordinary differential equations]] (ODEs). The ODEs can then be solved by any method. It has been shown that it is usually advantageous to choose the collocation points as the zeros of the corresponding [[Jacobi polynomial]] (independent of the PDE system).
== Notes ==
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