mws_mec_int_txt_romberg_examples

mws_mec_int_txt_romberg_examples - Chapter 07.05 Romberg...

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07.05.1 Chapter 07.05 Romberg Rule for Integration-More Examples Mechanical Engineering Example 1 A trunnion of diameter 3 36 . 12 has to be cooled from a room temperature of F 80 before it is shrink fit into a steel hub (Figure 1). Figure 1 Trunnion to be slid through the hub after contracting. The equation that gives the diametric contraction, in inches of the trunnion in dry-ice/alcohol (boiling temperature is F 108 ) is given by:  108 80 6 9 2 11 10 015 . 6 10 1946 . 6 10 2278 . 1 363 . 12 dT T T D Table 1 Values obtained for Trapezoidal rule. n Trapezoidal Rule 1 0.013536 2 0.013630 4 0.013679 8 0.013687 a) Use Romberg’s rule to find the contraction. Use the 2-segment and 4-segment Trapezoidal rule results given in Table 1. b) Find the true error, t E , for part (a). c) Find the absolute relative true error for part (a).

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07.05.2 Chapter 07.05 Solution a) in 013630 . 0 2
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mws_mec_int_txt_romberg_examples - Chapter 07.05 Romberg...

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