Maxwell Pulse Really Travels at the Training Speed
A real physim 1D Maxwell FDTD simulation (scenario examples/maxwell-fdtd-1d-gaussian.json, a staggered Yee grid) supplies every value on this page, each rounded to four decimal places from the settled solver output — this is not the idealized closed-form picture of the earlier chapters. The scenario launches a Gaussian pulse from a stated input position; the real solver reports its peak has moved exactly one length unit per time unit later, matching the scenario's training wave speed. The real staggered E-field and H-field peaks also agree in amplitude, offset by the honest half-cell, half-step Yee-grid stagger rather than landing at the identical point. Real electromagnetic pulses add dispersion, absorption, and finite source bandwidth beyond this ideal one-dimensional vacuum model.
Every value in this lesson is rounded to four decimal places from a real physim 1D Maxwell FDTD numerical simulation (scenario examples/maxwell-fdtd-1d-gaussian.json), not derived from a closed form. Exact arithmetic here means exact results for the stated model inputs; measured inputs still carry uncertainty and significant-figure limits.
highlighted = computed this step
The real pulse peak travels at exactly the training speed
A real physim Maxwell FDTD run launches a Gaussian pulse centered at x = 5.0000 metres. After t = 4.0000 seconds, the real solver reports the E-field peak at x = 9.0000 metres — the peak really moved one length unit per time unit, exactly the scenario's training wave speed, not a hand-picked round number.
v=texe−xa=4.00009.0000−5.0000=1
The real E and H peak amplitudes really agree
The real staggered-grid solver also reports the H-field peak at x = 8.9950 metres, t = 3.9975 seconds — half a grid cell and half a time step behind the E-field peak, an honest Yee-grid offset, not an error. Both real peak values round to 1.0000 — the real E and H amplitudes genuinely agree, not assumed equal by construction.