Galerkin Method

A method of determining coefficients 👁 alpha_k
in a power series solution

of the ordinary differential equation 👁 L^~[y(x)]=0
so that 👁 L^~[y(x)]
, the result of applying the ordinary differential operator to 👁 y(x)
, is orthogonal to every 👁 y_k(x)
for 👁 k=1
, ..., 👁 n
(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.

See also

Finite Element Method

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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.

Referenced on Wolfram|Alpha

Galerkin Method

Cite this as:

Weisstein, Eric W. "Galerkin Method." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/GalerkinMethod.html

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