Derives matching upper and lower bounds on absolute and relative discretization errors for centered FD on 1D Helmholtz via Fourier analysis under stated assumptions on k and h.
Compact 2D and 3D sixth order schemes for the Helmholtz equation with variable wave number.Journal of Computational Physics, 232(1):272–287
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Fourier Analysis of Finite Difference Schemes for the Helmholtz Equation in 1D with Dirichlet Conditions: Sharp Estimates and Relative Errors
Derives matching upper and lower bounds on absolute and relative discretization errors for centered FD on 1D Helmholtz via Fourier analysis under stated assumptions on k and h.