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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 == Suppose that the ordinary differential equation : is to be solved over the interval (). Choose 0 ≤ ''c''1< ''c''2< … < ''c''''n'' ≤ 1. The corresponding (polynomial) collocation method approximates the solution ''y'' by the polynomial ''p'' of degree ''n'' which satisfies the initial condition ''p''(''t''0) = ''y''0, and the differential equation ''p'' All these collocation methods are in fact implicit Runge–Kutta methods. The coefficient ''c''''k'' in the Butcher tableau of a Runge–Kutta method are the collocation points. However, not all implicit Runge–Kutta methods are collocation methods. 〔; 〕 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「collocation method」の詳細全文を読む スポンサード リンク
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