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mws_civ_int_txt_romberg_examples

mws_civ_int_txt_romberg_examples - 07.05 Romberg Rule for...

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07.05.1 07.05 Romberg Rule for Integration-More Examples Civil Engineering Example 1 The concentration of benzene at a critical location is given by 758 . 5 6560 . 0 75 . 1 73 . 32 erfc e erfc c where   dz e x erfc x z 2 So in the above formula dz e erfc z 6560 . 0 2 6560 . 0 Since 2 z e decays rapidly as z , we will approximate 6560 . 0 5 2 6560 . 0 dz e erfc z Table 1 Values obtained for Trapezoidal rule for 6560 . 0 5 2 6560 . 0 dz e erfc z n Trapezoidal Rule 1 1.4124 2 0.70695 4 0.40571 8 0.33475 a) Use Romberg’s rule to find 6560 . 0 erfc . 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). Solution a) 70695 . 0 2 I 40571 . 0 4 I Using Richardson’s extrapolation formula for Trapezoidal rule
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07.05.2 Chapter 07.05 3 2 2 n n n I I I TV and choosing 2 n , 3 2 4 4 I I I TV 3 70695 . 0 40571 . 0
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