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x 10 -3
2
1.8
1.6
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 8.5
0:5 of the function given by the sum of the first 100 terms of the
series defining the formal solution of the problem studied in Example 8.8
A snapshot at time t
D
x 10 -5
1.4
1.2
1
0.8
0.6
0.4
0.2
0
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
Fig. 8.6
1 of the function given by the sum of the first 100 terms of the
series defining the formal solution of the problem studied in Example 8.8
A snapshot at time t
D
becomes unstable for ˛>1=2. The reasoning will be based on a discrete analog to
the maximum principle, worked out in Sect. 8.1.5 .
Due to the boundary condition ( 8.2 ), the bounds of (8.41)-( 8.43 ) take the form
min min
x
f.x/;0 u .x; t / max max
x
f.x/;0 for all x 2 .0; 1/ and t 0;
 
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