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4
. TheODEsinth
iscaseare
dx
dt
=2
u
du
dt
=0
with
u
(
x,
0) =
f
(
x
)=
1
x<
0
1+
x
L
0
<x<L
2
L<x
a. Since the frst ODE contains
x
,
t
and
u
,weso
lvethesecondODEfrst
u
(
x, t
)=
u
(
x
(0)
,
0) =
f
(
x
(0))
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Unformatted text preview: dx dt = 2 f ( x (0)) The solution is x = x + 2 tf ( x )5 5 10 15 20 25 0.5 1 1.5 2 2.5 3 3.5 4 x t Figure 46: Characteristics ±or problem 4 237...
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This note was uploaded on 12/22/2011 for the course MAP 2302 taught by Professor Bell,d during the Fall '08 term at UNF.
 Fall '08
 BELL,D

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