This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
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 n1 ) ( 1 )~ ( ) + ( )( 1 ) (3) Plug in expanded g(p n1 ) 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 np n1 = ( 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...
View
Full
Document
This note was uploaded on 02/12/2012 for the course CHE 132b taught by Professor Ceweb during the Fall '09 term at UCSB.
 Fall '09
 Ceweb

Click to edit the document details