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ENGR 6101: Computational Engineering
Solution Set 4
(due on Wednesday in my mailbox by 4pm, 09/29)
Questions:
1. Consider the following ODE:
x
0
=
x
(1

x
)
x
(0) = 0
.
1
(a) (3 pts.) Find the analytic solution. Note that you can do this with separation of variables.
(b) (3 pts.) Write a Matlab code that solves this equation on the interval
[0
,
8]
using Euler
method. Your code should plot both the numerical and the analytic solution on the same
ﬁgure. Run your code with
h
= 1
and
h
= 2
. How does the accuracy change? Name
your code
ode_euler.m
and submit soft copy to
caner@uga.edu.
Include a hard copy
of your code (for
h
= 1
) and the two graphs (for
h
= 1
and
h
= 2
) along with your HW
solutions.
(c) (3 pts.) Repeat part (b) using second order Taylorseries method. In this case, name
your code
ode_taylor2.m
. Again, include both hard and soft copies of your code, and a
hard copy of the two graphs.
(d) (3 pts.) Repeat part (b) using second order RungeKutta method. In this case, name
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This note was uploaded on 03/16/2011 for the course ENGR 8101 taught by Professor Canor during the Fall '08 term at University of Georgia Athens.
 Fall '08
 CANOR

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