ps4solutions[1]

# ps4solutions[1] - APMA 2101 Problem Set#4 Sample Solution...

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

APMA 2101 Problem Set #4 Sample Solution Set (due 5 March 2009) Section 2.6.: The Euler Method (5 pts] Trying to get to the endpoint in just one step, h= 0.2, is trivial, y (0.2)=0. Of course, we expect the finest mesh step h =0.05 to be best, since all calculations use a method of the same fixed order. Section 6.1: The Imrpoved Euler Method [5 pts] 11. The exact solution, following the hint, is u(x) = tan(x+c) , or with the initial condition and a return to the original variables, y(x)=tan(x+ π /4)+1-x . Section 6.2: The Runge-Kutta Method [4 pts] Chapter 6: Supplementary Problems [4 pts (2 pts each)] (a) The solution of y’=Ay with y(0)=y 0 is y(t)=y 0 exp(At) , so y(t n )=y 0 exp(At n ), where t n =nh. The limit of the binomial expansion

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.

## This note was uploaded on 11/02/2009 for the course APMA 2102 taught by Professor Keyes during the Spring '08 term at Columbia.

### Page1 / 2

ps4solutions[1] - APMA 2101 Problem Set#4 Sample 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