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Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
book

Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition

by Andrei D. Polyanin, Vladimir E. Nazaikinskii
December 2015
Intermediate to advanced content levelIntermediate to advanced
1643 pages
59h 33m
English
Chapman and Hall/CRC
Content preview from Handbook of Linear Partial Differential Equations for Engineers and Scientists, 2nd Edition
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
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Publisher Resources

ISBN: 9781466581494