Euler Method - Exercise 1 Solution

Numerical Methods for Solving Differential Equations

Euler's Method

Using the Method withÌýMathematica

(continued fromÌýlast page...)

Solution to Exercise 1

Solution
Name		 Differential
Equation		 Initial
Condition		 Solve
up to		 Number
of Steps
eulerex1 ²â′Ìý=Ìýy y(0)Ìý=Ìý1 xÌý=Ìý1 10

Your solution, in tabular form, and abbreviated to save space, should have looked something like this:

0ÌýÌýÌýÌýÌýÌýÌýÌýÌý1
0.1ÌýÌýÌýÌýÌýÌýÌý1.1
0.2ÌýÌýÌýÌýÌýÌýÌý1.21
.ÌýÌýÌýÌýÌýÌýÌýÌýÌý.
.ÌýÌýÌýÌýÌýÌýÌýÌýÌý.
.ÌýÌýÌýÌýÌýÌýÌýÌýÌý.
0.9ÌýÌýÌýÌýÌýÌýÌý2.35795
1.ÌýÌýÌýÌýÌýÌýÌýÌý2.59374

And your plot of this solution should have looked something like this (though your points may not have been this size, or in color):

Euler Plot

If your solution doesn't match what you see here, then go back toÌýMathematicaÌýand carefully check the parameters that you passed to theÌýeulerÌýprogram. If necessary, change them, and reevaluate the commands.

±·´Ç·É,Ìýback to the exercises...

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