{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

128ahw9sum10

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

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

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 Taylor’s method of order two to approximate the solutions for each of the following initial-value problems. a. y 0 = te 3 t - 2 y , 0 t 1 y (0) = 0, with h = 0 . 5 Solution: Taylor’s 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 0 ( t i , w i ). In this problem, we have f ( t, y ) = te 3 t - 2 y and f 0 ( t, y ) = e 3 t +3 te 3 t - 2 y 0 = (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 + 0 . 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 + 0 . 5 T (2) ( t 0 , w 0 ) = 0 + 0 . 5 1 4 + 5 4 · 0 e 3 · 0 - 0 = 1 8 . and w 2 = w 1 + 0 . 5 T (2) ( t 1 , w 1 ) = 1 8 + 0 . 5 1 4 + 5 4 · 0 . 5 e 3 · 0 . 5 - 1 8 = 1 16 + 7 16 e 1 . 5 2 . 02324 . 2. Use Taylor’s method of order two to approximate the solutions for each of the following initial-value problems. a. y 0 = e t - y , 0 t 1, y (0) = 1, with h = 0 . 5 Solution: Taylor’s 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 0 ( t i , w i ).

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

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}