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 ...

The use of numerical tools to solve challenging problems in mathematics has exploded in the past several decades. The purpose of this paper is to compare the results of two different types of numerical methods in finding solutions to the eigenvalue problem for a second order elliptic partial differential equations (PDE) with boundary and transmission conditions. Transmission properties result f...