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This thesis presents a new technique to prove the convergence of finite difference methods applied to nonlinear Systems arising in computational fluid dynamics. The underlying Systems are either hyperbolic such as the Euler equations or mixed hyperbolic-parabolic like the Navier-Stokes equations. We analyze implicit finite-difference methods. As the argument is based on the concept of consistency

Direct and inverse scattering from dispersive media

Direct and inverse scattering from dispersive media are studied in the time domain. The media are one-dimensional and homogeneous but can be impedance mismatched to the surrounding media. A time domain method is introduced where the reflection and transmission kernels are obtained from Volterra equations of the second kind. Numerical examples are given based upon both synthetic and measured data f