Frequency response of 2nd and 4th order explicit and 4th-order implicit spatial derivatives. The receiver is located at x_r = [0.7, 0.8, 0.7]^T m and the source is located at x_s = [0.2, 0.4, 0.3]^T m. The analytical solution is shown in orange dashed and the numerical solution in blue. The gray area marks regions with a theoretical error (k’Δx − kΔx)_real > 10⁻³. The lower non-linear case shows results for high amplitudes, at 0.75 m distance from the source the peak magnitude of the blue line is at ≈146 dB_SPL and in light blue dashed at ≈152 dB_SPL.