Euler Method

odumath

New member
Joined
Sep 20, 2006
Messages
42
Hello,

I just started grad school ... and it's been a while since I took
Differential Equations.

One of our presentations dealed w/ the 'Euler Method'. Turns out that it is
the exact same problem as posted under the following URL:

http://www.math.duke.edu/education/ccp/ ... /sir3.html

We're tasked to do this problem in MS-Excel. Unfortunately, we've not been
given a great level of detailed instructions... guess it's coz we're on the
grad level.

Anyhow, I need some help as to how to compute the formula shown on the page
(URL). If you scroll down almost to the bottom of the page, the section
'the Euler formulas become' ... it then lists the 3 formulas.

I understand that I'm dealing w/ some constants and variables in this
problem. Could someone please help me how I can solve for the '1st
answer'... 1 step where time equals 0. The rest is done automatically in
Excel.

Let's say 's(0)' = 1. Do I calculate???

s sub n = s sub n -1 - 1/3 b etc..... or s sub n = 1 -1 - 1/3 b
 
You need a little setup.

First, starting values for each. You must set \(\displaystyle s_{0}, i_{0}, and r_{0}\), through experimentation or assumption.

Second, you must know your parameters b and k. You'll have to find them or get them from someone or from experimentation.

Third, you must pick a small time period. This can be very subjective. If you are talking about geology, 1000 years may be a suitably small period of time. Spread of disease may require days or hours. Management of a patient with cascading system failure may require minutes or seconds. Atomic reactions could require nanoseconds.

The Euler Method is a linear method. You should not expect exceptional results. They may be good enough for some models. Obviosuly, if you are studying it, there are useful purposes in your field. Generally, the smaller the time period, the better the results, but eventually you start to have rounding problems.
 
tkhunny,

thanks for the reply... ok, I do have the required values and parameters.

The problem suggests the following values:
S(0) = 7,900,00
I(0) = 10
R(0) = 0

s(0) = 1
i(0) = 1.27*10^-6
r(0) = 0

b = 1/2
k = 1/3

step size = 5

At this time, I'm just a bit rusting of "interpreting" the differential equation and "what to plug in where".

Reading the 1st formula, it begins with "s subscript n = s subscript n -1 - b ... etc"

Once I got the 1st entry/row (in Excel) going, I'll be fine.

So, again... my question is "how do I plug in those values". Be provide example of the 1st line given the constants/parameters given above.

Thanks!

Tom
 
Start with n = 1. Rewrite each equation with that.

n ==> 1
n-1 ==> 0

You should be able to figure it out.
 
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