128ahw11sum10

# 128ahw11sum10 - MATH 128A SUMMER 2010 HOMEWORK 11 SOLUTION...

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

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.

Unformatted text preview: MATH 128A, SUMMER 2010, HOMEWORK 11 SOLUTION BENJAMIN JOHNSON Homework 11: Due Monday, August 2 5.9; 4a 5.10; 1, 2a 5.11; 1a section 5.9 4. Use the Runge-Kutta for Systems Algorithm to approximate the solutions of the following higher-order differential equations, and compare the results to the actual solutions. a. y 00- 3 y + 2 y = 6 e- t , 0 ≤ t ≤ 1, y (0) = y (0) = 2, with h = 0 . 1 Solution: Let u 1 ( t ) = y ( t ) and u 2 ( t ) = y ( t ). Then u 1 ( t ) = y ( t ) = u 2 ( t ) and u 2 ( t ) = y 00 ( t ) = 6 e- t + 3 y- 2 y = 6 e- t + 3 u 2- 2 u 1 . We also have u 1 (0) = y (0) = 2 and u 2 (0) = y (0) = 2. The system of first-order IVP’s is thus: u 1 = u 2 , u 2 = 6 e- t + 3 u 2- 2 u 1 , ≤ t ≤ 1 , u 1 (0) = u 2 (0) = 2 . Using the online Java Interface for the Runge-Kutta for Systems Algorithm at http://www.as.ysu.edu/~faires/Numerical-Analysis/DiskMaterial/... programs/Java/Algo57.htm with N = 10, I got the following: Runge-Kutta Method for Systems with m = 2. T W1 W2 0.000000000 2.000000000 2.000000000 0.100000000 2.242468099 2.875595247 0.200000000 2.580967377 3.927146008 0.300000000 3.035177986 5.197761232 0.400000000 3.629545279 6.739956583 0.500000000 4.394323086 8.617777272 0.600000000 5.366851934 10.909389903 0.700000000 6.593124154 13.710247574 0.800000000 8.129699354 17.1369555360....
View Full Document

{[ snackBarMessage ]}

### Page1 / 3

128ahw11sum10 - MATH 128A SUMMER 2010 HOMEWORK 11 SOLUTION...

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

View Full Document
Ask a homework question - tutors are online