
24.2. Numerical Solutions of Linear PDEs 1387
By selecting the mesh and
Edit->Current Object Properties
, we can edit the plot ob-
tained (in the MATLAB graphics editor) and create the final plot shown in Fig. 24.5).
Example 24.7. Linear nonhomogeneous wave equation. Consider the initial-boundary value
problem for the two-dimensional linear wave equatio n
u
tt
= ν
2
(u
xx
+ u
yy
) + F(x, y,t), 0 < x < L
1
, 0 < y < L
2
, t > 0,
u(x,y,0) = w
1
(x,y), u
t
(x,y,0) = w
2
(x,y),
u(0,y,t) = 0, u(L
1
,y,t) = 0, u(x,0,t) = 0, u(x,L
2
,t) = 0,
describing th e vibrations of a membrane of length L
1
and wid th L
2
. Let u s find the displacement
function u(x,y,t). Le t L
1
= L
2
= π, ν = 1, F