MidtermSolution che 132b

MidtermSolution che 132b - ChE132B Midterm Exam Solutions...

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Unformatted text preview: ChE132B Midterm Exam Solutions 1. (a) ( 4 points ). If = 0, +1 = There will be no iteration at all. This is not an acceptable algorithm for finding a root. If = 1, +1 = ( ) The modified algorithm becomes the fixed point iteration again. (b) ( 18 points ). +1 = ( ) + (1 ) (1) = ( 1 ) + (1 ) 1 (2) Taylor expand g(p n-1 ) ( 1 )~ ( ) + ( )( 1 ) (3) Plug in expanded g(p n-1 ) back to Eq(2), ~ ( ) + ( )( 1 ) + (1 ) 1 (4) Rearrange = ( ) ( )( 1 ) + (1 ) 1 (5) Subtract Eq(5) from Eq(1) +1 = ( 1 )( 1 ) + (1 )( 1 ) (6) Divide both sides by p n-p n-1 = ( 1 ) + (1 ) (7) The absolute value of Eq(7) is the error ratio of this method. +1 = ( ) + (1 ) (8) as n goes to infinity, lim +1 = ( ) + (1 ) (9) Therefore, Order of convergence = 1 Asymptotic error constant = ( ) + (1...
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This note was uploaded on 02/12/2012 for the course CHE 132b taught by Professor Ceweb during the Fall '09 term at UCSB.

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MidtermSolution che 132b - ChE132B Midterm Exam Solutions...

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