Collocation method  From Wikipedia, the free encyclopedia Jump
to: navigation, search  In mathematics, a collocation method is
a method for the numerical solution of ordinary differential
equations, partial differential equations and integral
equations. The idea is to choose a finite-dimensional space of
candidate solutions (usually, polynomials up to a certain
degree) and a number of points in the domain (called collocation
points), and to select that solution which satisfies the given
equation at the collocation points.  Ordinary differential
equations[edit]  Suppose that the ordinary differential equation
is to be solved over the interval [t0t0 + h]. Choose 0 ≤ c1< c2<
… < cn ≤ 1.  The corresponding (polynomial) collocation method
approximates the solution y by the polynomial p of degree n
which satisfies the initial condition p(t0) = y0, and the
differential equation p'(t) = f(t,p(t)) at all points, called
the collocation points, t = t0 + ckh where k = 1, …, n. This
gives n + 1 conditions, which matches