A method of determining coefficients 
in a power series solution
 |
of the ordinary differential equation ![L^~[y(x)]=0](/images/equations/GalerkinMethod/Inline2.svg)
so that ![L^~[y(x)]](/images/equations/GalerkinMethod/Inline3.svg)
, 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.
