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Diferentiate (2) with respect to
x
twice
u
txx
=
−
cu
xxx
+ linear terms
Linear terms are enough because we have ∆
t
2
in Front. Also get
u
ttx
=
−
cu
xxt
+ linear terms
=
−
c
(
−
cu
xxx
) + linear terms
=
c
2
u
xxx
+ linear terms
u
ttt
=
−
cu
xtt
+ linear terms
=
−
c
3
u
xxx
+ linear terms
Substitute in (6)
u
t
=
−
cu
x
+
c
∆
t
2
4
c
2
u
xxx
−
c
2
u
xxx
+ linear terms
+
+∆
t
2
−
c
2
4
(
−
cu
xxx
+ linear terms) +
1
12
−
c
3
u
xxx
!
−
c
∆
x
2
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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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