The central topic of this thesis is the development and implementation of transparent boundary conditions for the time-dependent Bogoliubov-de Gennes equations. Both s- and p-wave systems are treated. The discretization of these equations is carried out within the Crank-Nicolson scheme. A general discretization strategy, introduced by van Dijk and Toyama for the Schrödinger equation, is adapted to the s-wave Bogloliubov-de Gennes equations. Numerical tests are restricted to hard boundary conditions. Another part of this thesis concerns itself with the construction and implementation of transparent boundary conditions in the general scheme mentioned above. This is done for the Schrödinger equation and only the spatial discretization is tackled. Throughout this thesis, numerical tests are employed to illustrate the results.