128a_su09_hw7_sol

128a_su09_hw7_sol - MATH 128A, SUMMER 2009: HOMEWORK 7...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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....
View Full Document

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.

Page1 / 2

128a_su09_hw7_sol - MATH 128A, SUMMER 2009: HOMEWORK 7...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online