What is the advantage of using fourier series in the spectral method?

What is the advantage of using fourier series in the spectral method? Correct Answer Continuous results

The Fourier series can be interpolated to get the dependent function. This will help us to get the results at a continuous space instead of results at particular grid points. This is an advantage over the other discretization techniques.
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Related Questions

Let x(t) be a continuous time periodic signal with fundamental period T = 1 seconds. Let {ak} be the complex Fourier series coefficients of x(t), where k is integer valued. Consider the following statements about x(3t):
1. The complex Fourier series coefficients of x(3t) are {ak} where k is integer valued.
2. The complex Fourier series coefficients of x(3f) are {3ak} where k is integer valued.
3. The fundamental angular frequency of x(3t) is 6π rad/s.
For the three statements above, which one of the following is correct?
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