Chequerboard Modes And The Generalized Lax-Friedrichs Schemes For Hyperbolic Conservation Laws

In this thesis we analyze chequerboard modes existing in the generalized Lax-Friedrichs (LxF) schemes for computing of hyperbolic conservation laws. This analysis helps to understand the generalized LxF schemes in the resolution of high frequency modes and to explain the oscillations presenting in numerical solutions when initial data are discretized improperly.We analyze the presence of chequerboard modes from the discretization of initial data. Then we proceed to use the modified equation analysis to investigate the generalized LxF schemes in the resolution of aforementioned chequerboard modes.