Fourier symbol of a difference operator
= Fourier symbol of a difference operator
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= Fourier symbol
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For a translation-invariant difference operator $(Lu)_m=\sum_j a_j u_{m+j}$, its Fourier symbol is $\ell(\theta)=\sum_j a_je^{ij\theta}$. Applying $L$ to a <Fourier mode> $e^{im\theta}$ multiplies that mode by $\ell(\theta)$. Symbols turn constant-coefficient stencil equations into scalar algebraic equations and expose their <Von Neumann stability analysis>.