  This paper is devoted to the study of the inhomogeneous wave equation with
singular (less than continuous) time dependent coefficients. Particular
attention is given to the role of the lower order terms and suitable Levi
conditions are formulated in order to obtain a very weak solution as introduced
in \cite{GR:14}. Very weak solutions for this kind of equations are also
investigated from a numerical point of view in two toy models: the wave
equation with a Heaviside function and a delta distribution, respectively, as
coefficient in its principal part.
