Convergence of difference approximations for initial- and mixed boundary-value problems for the wave equation

In this thesis we describe the finite difference scheme that approximates the solution of the one-dimensional wave equation subject to mixed boundary- and initial conditions. We derive an error estimate for the scheme, in the discrete l. 2-norm, for which we prove the convergence to be of order (k² + h^3/2) , and finally we report on the numerical experiments we performed using the scheme.