An important approach to the numerical solution of ordinary differential and integral equations. Approximations are obtained on the basis that the equation is satisfied exactly at a particular set of points in the given problem range. For example, for
an approximation
can be obtained from a suitable set of orthogonal functions ϕ
i(
x) by choosing the coefficients α
i for which
for some set of collocation points
Initial conditions and boundary conditions may also be incorporated into the process.