N35 - ME – 510 NUMERICAL METHODS FOR ME II ADAMS-MOULTON

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Unformatted text preview: ME – 510 NUMERICAL METHODS FOR ME II ADAMS-MOULTON PREDICTOR-CORRECTOR METHODS Order Predictor-Corrector Formulae Local Error y p 1 n 2 y c 1 n y p 1 n 3 y c 1 n y p 1 n 4 y c 1 n h 3 f n - f n -1 2 h y n  f np1  f n 2 h y n  23 f n - 16 f n -1  5 f n - 2 12 h y n  5 f np1  8 f n - f n -1 12 h y n  55 f n - 59 f n -1  37 f n -2 - 9 f n -3 24 h y n  9 f np1  19 f n - 5 f n -1  f n -2 24 yn  E n 1 # 1p y n 1 - y c 1 n 6 E n 1 # 1p y n 1 - y c 1 n 10 E n 1 # 19 p y n 1 - y c 1 n 270 3URI 'U )DUXN $UÕQo Fall 2007 ME – 510 NUMERICAL METHODS FOR ME II ADAMS-MOULTON CLOSED FORMULAE n y i 1 Order of the Formula (n) k=1 D n1 k=2 Dn2 yi  h ¦ D nk k 1 f i - k 1  O(h n 1 ) k=5 Dn5 k=6 Dn6 Local Truncation Error, O(hn+1) 12 h f ' ( [) 2 k=3 Dn3 k=4 Dn4 1 1 2 1 2 5 12 9 24 251 720 475 1440 1 2 8 12 19 24 646 720 1427 1440 1 12 5 24 264 720 1 24 106 720 482 1440 - - 13 h f ' ' ( [) 12 14 h f ' ' ' ( [) 24 19 5 (4) hf ( [) 720 3 - 4 - - 5 - 19 720 173 1440 - 27 h 6 f (5) ([) 1440 863 h 7 f (6) ([) 60480 6 798 1440 27 1440 - 3URI 'U )DUXN $UÕQo Fall 2007 ...
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This note was uploaded on 02/28/2011 for the course ME 510 taught by Professor Dr.faruckarinc during the Spring '11 term at Middle East Technical University.

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