128ahw9sum10 - MATH 128A, SUMMER 2010, HOMEWORK 9 SOLUTION...

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Unformatted text preview: MATH 128A, SUMMER 2010, HOMEWORK 9 SOLUTION BENJAMIN JOHNSON Homework 9: Due Monday, July 26 5.3; 2a, 5b 5.4; 1b, 5b 5.5; 1d section 5.3 1. [Not Assigned included in the solution for your benefit because I did it by accident :)] Use Taylors method of order two to approximate the solutions for each of the following initial-value problems. a. y = te 3 t- 2 y , 0 t 1 y (0) = 0, with h = 0 . 5 Solution: Taylors order two method uses w i +1 = w i + hT (2) ( t i ,w i ) where T (2) ( t i ,w i ) = f ( t i ,w i ) + h 2 f ( t i ,w i ). In this problem, we have f ( t,y ) = te 3 t- 2 y and f ( t,y ) = e 3 t +3 te 3 t- 2 y = (1+3 t ) e 3 t- 2( te 3 t- 2 y ) = (1 + t ) e 3 t + 4 y . So T (2) ( t i ,w i ) = te 3 t i- 2 w i + . 5 2 ((1 + t i ) e 3 t i + 4 w i ) = ( 1 4 + 5 4 t i ) e 3 t i- w i . So w 1 = w + 0 . 5 T (2) ( t ,w ) = 0 + 0 . 5 1 4 + 5 4 e 3 - = 1 8 . and w 2 = w 1 + 0 . 5 T (2) ( t 1 ,w 1 ) = 1 8 + 0 . 5 1 4 + 5 4 . 5 e 3 . 5- 1 8 = 1 16 + 7 16 e 1 . 5 2 . 02324 . 2. Use Taylors method of order two to approximate the solutions for each of the following initial-value problems. a. y = e t- y , 0 t 1, y (0) = 1, with h = 0 . 5 Solution: Taylors order two method uses w i +1 = w i + hT (2) ( t i ,w i ) where T (2) ( t i ,w i ) = f ( t i ,w i ) + h 2 f ( t i ,w i )....
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This note was uploaded on 01/04/2011 for the course MATH 128A taught by Professor To during the Fall '10 term at SUNY Geneseo.

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128ahw9sum10 - MATH 128A, SUMMER 2010, HOMEWORK 9 SOLUTION...

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