
Chapter 24
Linear Partial Differential
Equations with MATLAB
R
24.1 In troductio n
In the previous two chapters, we paid special attention to analytical solutions of linear par-
tial 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 prob-
lems 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 Thom´ee (2008), Lax (1968), ...