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{c}

For the two-periodic problem
$$
-\frac{1+2\cos\pi x}{\pi^2}u''+u=f,
$$
the Fourier coefficients satisfy the tridiagonal system
$$
(m-1)^2\widehat u_{m-1}
+(m^2+1)\widehat u_m
+(m+1)^2\widehat u_{m+1}
=\widehat f_m,
\qquad m\in\mathbb Z.
$$


Fourier spectral system for a cosine-modulated second derivative

Past exam of the mathematics course of the University of Cambridge / 2019 / ii / Paper 4 / 39C / a / Solution

Fourier spectral system for a cosine-modulated second derivative

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Fourier spectral system for a cosine-modulated second derivative

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