Magnonics-an emerging field of physics-is based on the collective excitations of ordered spins called spin waves. These low-energy excitations carry pure spin currents, paving the way for future technological devices working at low energies and on ultrafast timescales. The traditional ab−initio approach to predict these spin-wave energies is based on linear-response time-dependent density functional theory (LR-TDDFT) in the momentum and frequency regime. Herein, the simulation of magnon dynamics using real-time time-dependent density functional theory is demonstrated, thus extending the domain of ab-initio magnonic studies. Unlike LR-TDDFT, this enables us to observe atom-resolved dynamics of individual magnon modes and, using a supercell approach, the dynamics of several magnon modes can be observed simultaneously. The energies of these magnon modes are concurrent with those found using LR-TDDFT. Next, the complex dynamics of the superposition of magnon modes is studied, before finally studying the element-resolved modes in multisublattice magnetic systems.