156_pdfsam_math 54 differential equation solutions odd

# 156_pdfsam_math 54 differential equation solutions odd -...

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Chapter 3 Table 3–G : Improved Euler’s method to approximate the temperature in a building over a 24-hour period (with K =0 . 2). Time t n t n t T n T T n Midnight 0 65 12:40 a.m. 0.6667 66.63803 1:20 a.m. 1.3333 67.52906 2:00 a.m. 2.0000 68.07270 2:40 a.m. 2.6667 68.46956 3:20 a.m. 3.3333 68.81808 4:00 a.m. 4.0000 69.16392 8:00 a.m. 8.0000 71.48357 Noon 12.000 72.90891 4:00 p.m. 16.000 72.07140 8:00 p.m. 20.000 69.80953 Midnight 24.000 68.38519 Recalling that t 0 is midnight, we see that these results imply that at 0 . 6667 hours after midnight (or 12 : 40 a.m. ) the temperature is approximately 66 . 638 . Continuing with this process for n =1 , 2 ,..., 35 gives us the approximate temperatures in a building with K =0 . 2 over a 24 hr period. These results are given in Table 3-G. (This is just a partial table.)
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Unformatted text preview: The next step is to redo the above work with K = 0 . 4. That is, we substitute K = 0 . 4 and h = 2 / 3 ≈ . 6667 into equations (3.17) and (3.18) above. This yields F = 135 . 1 − 8 cos ± πt 12 ² − 1 . 9 T, G = 135 . 1 − 8 cos ³ π ( t + 0 . 6667) 12 ´ − 1 . 9( T + 0 . 6667 F ) , and T = T + (0 . 3333)( F + G ) . Then, using these equations, we go through the process of Frst Fnding F , then using this result to Fnd G , and Fnally using both results to Fnd T . (This process must be done for 152...
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