Question

Spectral methods use ___________

(a) Fourier series

(b) Taylor series

(c) McLaurin series

(d) Laurent series

I had been asked this question by my school teacher while I was bunking the class.

Question is from Finite Difference Methods in chapter Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Correct option is (a) Fourier series

For explanation: Finite Difference methods use Taylor series. In spectral methods, spatial derivatives are evaluated using the Fourier series or one of their generalization. The simplest spectral methods deal with periodic functions specified by their values at a uniformly spaced set of points.