  This thesis aims at investigating the first steps toward an unconditionally
stable space-time isogeometric method, based on splines of maximal regularity,
for the linear acoustic wave equation. The unconditional stability of
space-time discretizations for wave propagation problems is a topic of
significant interest, by virtue of the advantages of space-time methods
compared with more standard time-stepping techniques. In the case of continuous
finite element methods, several stabilizations have been proposed. Inspired by
one of these works, we address the stability issue by studying the isogeometric
method for an ordinary differential equation closely related to the wave
equation. As a result, we provide a stabilized isogeometric method whose
effectiveness is supported by numerical tests. Motivated by these results, we
conclude by suggesting an extension of this stabilization tool to the
space-time isogeometric formulation of the acoustic wave equation.
