Euler Method - Exercise 2 Solution

Numerical Methods for Solving Differential Equations

Euler's Method

Using the Method with Mathematica

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Solution to Exercise 2

Solution
Name		 Differential
Equation		 Initial
Condition		 Solve
up to		 Number
of Steps
eulerex2 y′ = x - y y(0) = 0.5 x = 1 20

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

0          0.5
0.05       0.475
0.1        0.45375
.          .
.          .
.          .
0.95       0.51603
1.         0.537729

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 to Mathematica and carefully check the parameters that you passed to the euler program. If necessary, change them, and reevaluate the commands.

Now, back to the exercises...

 

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