Math 293, Homework 8
due in lecture on Wednesday October 23, 1996.
(*) = don't hand in
*) You should be able to do problems of the form 5.2.1-37
1) 5.2.13. Pick and state some initial condition and find
c1 and c2 to satisfy that initial condition.
2) Let x(t) = [ x1(t) x2(t) x3(t) x4(t) ]' where []' is the transpose of [].
A = [ -10 -2 3 -4;
5 -6 7 -8;
1 -2 3 5;
e -pi 1 -1 ] ;
( where pi=3.1415... and ln(e) = 1 )
You are given that x satisfies the system of ODEs x' = A x
and the initial condition x(0) = [ 0 0 1 -3 ]'
a) Find x(2) using the eigenvalue and eigenvector method.
That is find the 4 numbers x1(2), x2(2), x3(2), and x4(2).
You may assume, correctly, that A has 4 eigenvectors.
(The course WWW page has enough samples to get you through
the needed MATLAB commands. The text and lecture indicate
the recipe that is to be applied.)
Hand in a tidy script file, not a rambling interactive
session of commands.)
b) Find x(2) using ODE23 or ODE45.
(If any of your 4 answers from parts (a) and (b) differ
by more than a percent you have made a mistake.)
c) Optional challenge 1:
How close can you get the answers of (a) and (b)?
At that accuracy which takes less computer time to find?
d) Optional challenge 2:
How compact can you make your solutions?