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Unformatted text preview: MATH 128A, SUMMER 2009: HOMEWORK 7 SOLUTIONS (1) Lets use the notation w AB3 for the Adams-Bashforth(3) predictors estimate of y i +1 , w AM2 for the Adams-Moulton(2) correctors estimate of y i +1 , and AB3 and AM2 for their respective truncation errors. From the textbook, we have the truncation error formulas AB3 = y i +1- w AB3 h = 3 8 y (4) ( AB3 ) h 3 , AB3 [ t i- 2 ,t i +1 ] AM2 = y i +1- w AM2 h - 1 24 y (4) ( AM2 ) h 3 , AM2 [ t i- 1 ,t i +1 ] (Technically speaking, the equation in the second line is approximate: it gives the predictor- corrector methods truncation error as that of the corrector step. The difference ends up being O ( h 4 ), and may be ignored.) Proceed by assuming that y (4) ( ) is approximately constant on the relevant interval. When we subtract the equations, the y i +1 terms cancel and were left with w AM2- w AB3 h 10 24 y (4) (?) h 3 The left-hand side is- 1, so y (4) (?) h 3 - 24 / 10. Plugging back into the formula for10....
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This note was uploaded on 04/06/2010 for the course MATH various taught by Professor Tao/analysis during the Spring '10 term at UCLA.
- Spring '10