Euler Method - Using the Method with Mathematica - Part 6

Numerical Methods for Solving Differential Equations

Euler's Method

Using the Method with Mathematica

(continued from last page...)

I've abbreviated the output a little here, in order to save space. You should have gotten the long version of:

prelimsol3=euler[x+2y, {x, 0, 1}, {y, 0}, 100]

{{0, 0}, {0.01, 0}, {0.02, 0.0001}, {0.03, 0.000302},
   {0.04, 0.00060804}, {0.05, 0.0010202}, {0.06, 0.0015406},
   .
   .
   .
   {0.95, 0.915425}, {0.96, 0.943233}, {0.97, 0.971698},
   {0.98, 1.00083}, {0.99, 1.03065}, {1., 1.06116}}

MatrixForm[prelimsol3]

0            0
0.01         0
0.02         0.0001
0.03         0.000302
.            .
.            .
.            .
0.98         1.00083
0.99         1.03065
1.           1.06116

So, our new last point is (1.00, 1.06116), which is much closer to the correct result of (1.00, 1.097264), but is still not perfect. Clearly if we wanted even greater accuracy, we could ask the computer for even more steps—if we were willing to wait for the calculations to finish. I don't think we'll bother, however.

Let's go and have you try some exercises on your own instead...

If you're lost, impatient, want an overview of this laboratory assignment, or maybe even all three, you can click on the compass button on the left to go to the table of contents for this laboratory assignment.