  We demonstrate an application of the spectral method as a numerical
approximation for solving Hyperbolic PDEs. In this method a finite basis is
used for approximating the solutions. In particular, we demonstrate a set of
such solutions for cases which would be otherwise almost impossible to solve by
the more routine methods such as the Finite Difference Method. Eigenvalue
problems are included in the class of PDEs that are solvable by this method.
Although any complete orthonormal basis can be used, we discuss two
particularly interesting bases: the Fourier basis and the quantum oscillator
eigenfunction basis. We compare and discuss the relative advantages of each of
these two bases.
