course | course_year | question_number | tags | title | year | |||
---|---|---|---|---|---|---|---|---|
Numerical Analysis |
II |
104 |
|
Paper 4, Section II, C |
2013 |
Consider the solution of the two-point boundary value problem
with periodic boundary conditions at
The Fourier coefficients of
$$\hat{u}{n}=\frac{1}{2} \int{-1}^{1} u(\tau) e^{-i \pi n \tau} d \tau$$
Prove that the computation of the Fourier coefficients for the truncated system with
Explain the term convergence with spectral speed and justify its validity for the derived approximation of