文摘
英文文摘
首都师范大学学位论文原创性声明及授权使用声明
Chapter 1Introduction
1.1 Backgrounds
1.2 Structure of the thesis
1.3 Preliminaries and notations
1.3.1 The chequerboard mode
1.3.2 Modified equation analysis
Chapter 2 Local oscillations in the solutions by the generalized Lax-Friedriches schemes
2.1 Examples of the linear hyperbolic conserva-tion laws
2.2 Examples of the nonlinear hyperbolic con-servation laws
Chapter 3 Chequerboard modes in the initial discretization
3.1 Single square signal case
3.2 Discretization of general initial data
Chapter 4 Analysis of the evolution of the chequerboard mode by the generalized Lax-Friedrichs schemes
4.1 Modified equation analysis for the linear equations
4.2 Conlusions
Chapter 5 Two spatial dimensions
5.1 Numerical experiments
5.2 Discrete Fourier analysis
5.2.1 Single square signal case
5.2.2 For the Linear advection equation
5.3 Modified equation analysis
Bibliography
ACKNOWLEDGEMENT
首都师范大学;