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Applied Calculus of Variations for Engineers, 2nd Edition
book

Applied Calculus of Variations for Engineers, 2nd Edition

by Louis Komzsik
June 2014
Intermediate to advanced content levelIntermediate to advanced
233 pages
5h 42m
English
CRC Press
Content preview from Applied Calculus of Variations for Engineers, 2nd Edition
94 Applied calculus of variations for engineers
0
0
.2
0
.4
0
.6
0
.8
1
1.2
1.4
1.6
0 0.2 0.4 0.6 0.8 1
y_approx(x)
y_exact(x)
y_error(x)
FIGURE 7.1 Accuracy of the Ritz solution
The figure demonstrates that the Ritz solution satisfies the boundary con-
ditions and shows acceptable differences in the interior of the interval. Finally,
the variational problem’s extremum is computed for both cases. The analyt-
ical solution is based on the derivative
y
=
2πcos(πx),
and obtained as
1
0
y
2
(x)dx =2π
2
1
0
cos
2
(πx)dx = π
2
=9.87.
The Ritz solution’s derivative is
y
=
30(2x 1).
and the approximate extremum is
1
0
y
2
(x)dx =30
1
0
(2x 1)
2
dx =
30
3
=10.
The approximate extremum
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Publisher Resources

ISBN: 9781482253597