  For strongly anisotropic time-reversal invariant (TRI) insulators in two and
three dimensions, the band inversion can occur respectively at all TRI momenta
of a high symmetry axis and plane. Although these classes of materials are
topologically trivial as the strong and weak $Z_{2}$ indices are all trivial,
they can host an even number of unprotected helical gapless edge states or
surface Dirac cones on some boundaries. We show in this work that when the
gapless boundary states are gapped by $s_{\pm}$-wave superconductivity, a
boundary time-reversal invariant topological superconductor (BTRITSC)
characterized by a $Z_{2}$ invariant can be realized on the corresponding
boundary. Since the dimension of the BTRITSC is lower than the bulk by one, the
whole system is a second-order TRI topological superconductor. When the
boundary of the BTRITSC is further cut open, Majorana Kramers pairs and helical
gapless Majorana modes will respectively appear at the corners and hinges of
the considered sample in two and three dimensions. Furthermore, a magnetic
field can gap the helical Majorana hinge modes of the three-dimensional
second-order TRI topological superconductor and lead to the realization of a
third-order topological superconductor with Majorana corner modes. Our proposal
can potentially be realized in insulator-superconductor heterostructures and
iron-based superconductors whose normal states take the desired inverted band
structures.
