Common Difference Schemes for Several Model Equations

This chapter discusses common difference schemes for several model equations, including one-dimensional advection equations, diffusion equations, and convection diffusion equations. For each difference scheme, its difference equation, amplification matrix, stability conditions, and truncation error are given, and they are summarized and compared with tables and figures. The advantages and disadvantages of different difference schemes and their application ranges are analyzed, and some issues that need attention are pointed out, such as compatibility, accuracy, computational complexity, and initial conditions.