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# 25 2 05 04 03 3 055 045 0338 4 06 0506 0338 5

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Unformatted text preview: .25 -0.15 -0.063 -0.013 0.0 0.0 4 -0.6 -0.5 -0.4 -0.3 -0.2 -0.106 -0.038 -0.006 0.0 5 -0.65 -0.55 -0.45 -0.35 -0.25 -0.153 -0.072 -0.022 -0.003 Table 2.2.2: Solution of Example 2.2.1 using the forward time-backward space scheme (2.2.4). of the forward time-forward space scheme (2.2.2b). To rule out the possibility that the problems could be due to a lack of smoothness in the data and to further study the performance of these two schemes, let us study a second example. Example 2.2.2. Consider (2.2.1) with = 1 and a ( ) = sin x x hence, the exact solution is the traveling sinusoidal wave ( ) = sin( ; ) uxt x t: We'll solve this initial value problem on 0 2 using = 2 16 and = 2 32, n so j = 1 2. Solutions of the forward time-forward space (2.2.2b) and forward timebackward space (2.2.4) schemes are shown in Figure 2.2.4. The forward space scheme appears to be working however, its solution is increasing in amplitude. Oscillations are not present on this time scale but would appear had we computed for...
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