Fourier Analysis of Finite Difference Schemes for the Helmholtz Equation in 1D with Dirichlet Conditions: Sharp Estimates and Relative Errors

Martin J. Gander, Hui Zhang, Haiyang Zhou

We consider the Dirichlet problem of the indefinite Helmholtz equation in 1D, $u^{\prime \prime }+k^{2}u=f$ in $(0,1)$, $u(0)=g_0$, $u(1)=g_1$, with a constant wavenumber $k\in(0,\infty)\backslashÏ…