 Fourier spectral system for a cosine-modulated second derivative

ID: fourier-spectral-system-for-a-cosine-modulated-second-derivative

For the two-periodic problem

- \frac{1 + 2 c o s π x}{π ^{2}} u^{''} + u = f,

the Fourier coefficients satisfy the tridiagonal system

(m - 1)^{2} u_{m - 1} + (m^{2} + 1) u_{m} + (m + 1)^{2} u_{m + 1} = f_{m}, m \in Z .

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