Galerkin Method

A method of determining coefficients  in a power series solution

of the ordinary differential equation  so that , the result of applying the ordinary differential operator to , is orthogonal to every  for , ...,  (Itô 1980).

Galerkin methods are equally ubiquitous in the solution of partial differential equations, and in fact form the basis for the finite element method.

REFERENCES:

Itô, K. (Ed.). "Methods Other than Difference Methods." §303I in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 2. Cambridge, MA: MIT Press, p. 1139, 1980.