Many-particle time domain methods are rising alternatives to particle-in-cell (PIC) or frequency methods to simulate the wave–beam interactions in traveling wave tubes (TWTs). We focus on two of those: our Hamiltonian discrete model DIMOHA is compared analytically against the pseudospectral method RUBEUS. Although based on two completely different approaches—the Gel’fand transform for DIMOHA and the telegraphist circuit for RUBEUS—we surprisingly find out that they share perfectly parallel sets of equations and variables. However, we conclude that DIMOHA is more flexible than RUBEUS in terms of pitch tapering and absorbing boundary conditions. It also shows excellent stability for steady-state simulation, allowing us to explain some discrepancies of RUBEUS with experimental results. These come from a standing wave pattern which is detectable in the vicinity of the sever. Finally, DIMOHA is tested for the first time with ultra-short pulses and exhibits excellent agreement with RUBEUS.