Question

Spectral methods are much more accurate than the Finite Difference methods ___________

(a) unconditionally

(b) conditionally depending on the problem taken

(c) conditionally when the number of grid points is small

(d) conditionally when grid size is small

I have been asked this question in a job interview.

Enquiry is from Finite Difference Methods in section Finite Difference Methods of Computational Fluid Dynamics

Answer 1

Right choice is (d) conditionally when grid size is small

To explain: The error in the solution decreases exponentially with the number of grid points. The results are more precise when the number of grid points is more. So, the grid size should be small. This makes the spectral method with more grids accurate than the Finite Difference methods.