ABSTRACT
In the previous two chapters, we paid special attention to analytical solutions of linear partial differential equations and systems in the context of computer algebra systems Maple and Mathematica. However, in real-world problems, the functions and data in PDE problems are often defined at discrete points and the equations are too complicated, so that it is not possible to construct analytical solutions. Therefore, one has to study and develop numerical approximation methods for linear PDEs [e.g., see Crank and Nicolson (1947), Larsson and Thome´e (2008), Lax (1968), LeVeque (2007), Li and Chen (2009)].
