Stability analysis of second order finite difference schemes for parabolic and hyperbolic equations

In this work we are concerned with second order finite difference schemes that are applied to two model equations. We examine stability restrictions for such schemes using linear and nonlinear stability analysis. A simple method is proposed for investigating the computational stability (linear and nonlinear) of finite difference equations. For the Hyperbolic model, the resulting difference equations are analyzed in terms of dispersion relation and propagation properties. The effect of the boundary conditions is discussed. (author). 9 refs., 3 figs