### spectral method

(method of numerically solving differential equations)

A **spectral method** is a method of numerically solving differential
equations by approximating the equations using, for example, a
**Fourier series**, and solving each term. Typically a Fourier transform
is used.

A typically-used fourier series describes a function over a finite
interval (or a function that repeats over such an interval) as a
potentially infinite series of sine functions at various frequencies
and phases. If a finite subset of these sine functions sums to a
good approximation of the function, then differentials of this set
of sine functions may sum to a good approximation of differentials
of the function in question.

(*mathematics,computation*)
**Further reading:**

http://en.wikipedia.org/wiki/Spectral_method

**Referenced by pages:**

numerical analysis

SpEC

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