Solving Systems

Solving the Preliminary Example

(continued from last page...)

Your new combined picture should look like this:

Show[prelimxplot,proposedxplot]

What happened to the red and blue graphs? Well, they didn't disappear, they just overlap each other, making a purplish one! That's how close the two solutions are to one another! Now the blue one we know is definitely a valid solution. After all, we spent the first part of this laboratory substituting this proposed solution into the differential equations just to make sure that it works. The fact that the red graph follows the blue one so closely should give us some confidence in Mathematica's numerical solver routines.

Now it's time for you to try something on your own. I just went through the graphical comparison of the two x-components of both the numerical solution and the original proposed solution. Now you do the same for the y-components. This will be a multi-step process, but I think you can handle it. (You can go back and recap the steps I took if you need to.) Don't forget to return here when you're done.

We'll now go look at what you should have gotten...

 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.

ODE Laboratories: A Sabbatical Project by Christopher A. Barker

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