
1392 LINEAR PARTIAL DIFFERENTIAL EQUATIONS W ITH MATLAB
R
0 0.2 0.4 0.6 0.8 1
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Solution profile at t
k
= 0.004, 0.2, 0.4
t=0.004
t=0.2
t=0.4
Figure 24.9 Linear diffusion–convection equation: solution profiles at t
k
= 0.004, 0.2, 0.4.
24.3 C onstructing Finite Differenc e Approximations
Now we show the helpful role of MATLAB when applying and developing various finite
difference approximations to construct numerical solutions of initial value problems and
initial-boundary value problems for linear PDE s (e.g., parabolic and hyperbolic equations)
[for details, see Li and Chen (2009), Mathews and Fink (1999), Yang, Cao, Chung, and ...