  We develop a formalism for modelling exact time dynamics in waveguide quantum
electrodynamics (QED) using the real-space approach. The formalism does not
assume any specific configuration of emitters and allows the study of Markovian
dynamics fully analytically and non-Markovian dynamics semi-analytically with a
simple numerical integration step. We use the formalism to study subradiance,
superradiance and bound states in continuum. We discuss new phenomena such as
subdivision of collective decay rates into symmetric and anti-symmetric subsets
and non-Markovian superradiance effects that can lead to collective decay
stronger than Dicke superradiance. We also discuss possible applications such
as pulse-shaping and coherent absorption. We thus broaden the range of
applicability of real-space approaches beyond steady-state photon transport.
