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Numerically solving ordinary differential equations online

I'm teaching a class on ordinary differential equations (ODE). What's a nice website where students can easily type in a first-order ODE and an initial value and get a graph of the solution?

I'd prefer a program that uses the Euler scheme, because it's easy to explain, and I'd prefer it if you can choose the step size. But the most important thing is ease of use.

We have Mathematica on the math department computers, and our math majors can in principal use that, but for a class of 90 this is not very practical: it would overwhelm the rather small facilities. Also, it would require teaching them a bit of Mathematica, which would steal from the limited time we have for this.

Another possibility is the Khan Academy computer science website---see for example this program. If I (or you) could write the desired program here, everyone in the world could use it---and if they register, also modify it and make new versions.

Comments

  • 1.

    Do you have access to Matlab? Better yet, the Matlab compiler?

    I can't promise, but if you did, there is a chance I could build a little GUI-based application for you.

    Someone else here may be able to easily convert it to javascript or something.

    Just thinking out loud...

    Comment Source:Do you have access to Matlab? Better yet, the Matlab compiler? I can't promise, but if you did, there is a chance I could build a little GUI-based application for you. Someone else here may be able to easily convert it to javascript or something. Just thinking out loud...
  • 2.

    Thanks, Eric, but it looks like I'm doing okay now with a combination of this:

    and a program Mike Stay wrote, with minor tweaks of my own:

    The second one is nice because 1) you can see the guts of the program and modify them and 2) you can save the modified version and other people can use it.

    If someone knows the language being used here (Python, I guess???) it would be nice if they could put labelled axes on the graph and show the coordinates of the cursor. That would make it a much better tool for homework assignments.

    Comment Source:Thanks, Eric, but it looks like I'm doing okay now with a combination of this: * Jonathan R. Senning, [First order differential equation solver](http://www.math-cs.gordon.edu/~senning/desolver/). and a program Mike Stay wrote, with minor tweaks of my own: * [ODE solver](http://www.khanacademy.org/cs/ode2/1077487275), Khan Academy. The second one is nice because 1) you can see the guts of the program and modify them and 2) you can save the modified version and other people can use it. If someone knows the language being used here (Python, I guess???) it would be nice if they could put labelled axes on the graph and show the coordinates of the cursor. That would make it a much better tool for homework assignments.
  • 3.
    nad
    edited October 2012

    If someone knows the language being used here (Python, I guess???) it would be nice if they could put labelled axes on the graph and show the coordinates of the cursor. That would make it a much better tool for homework assignments.

    I think this is javascript, but I am not sure. In the same way I forget the wikicommands I tend to forget the various syntaxes of the respective programming languages.

    anyways, I made some axes now. I had problems with the coordinates for the mouse though, since I couldn't find out in a decent time how to turn a real into a string (this may actually not possible in javascript since I think to remember there was something awkward with typing). If you find out you can plug that in where the mousebuttontext is. If not you probably should erase this mousebuttontext, as it would probably appear as too silly to leave it there...

    the code is at http://www.khanacademy.org/cs/ode21/1077726566

    Comment Source:>If someone knows the language being used here (Python, I guess???) it would be nice if they could put labelled axes on the graph and show the coordinates of the cursor. That would make it a much better tool for homework assignments. I think this is javascript, but I am not sure. In the same way I forget the wikicommands I tend to forget the various syntaxes of the respective programming languages. anyways, I made some axes now. I had problems with the coordinates for the mouse though, since I couldn't find out in a decent time how to turn a real into a string (this may actually not possible in javascript since I think to remember there was something awkward with typing). If you find out you can plug that in where the mousebuttontext is. If not you probably should erase this mousebuttontext, as it would probably appear as too silly to leave it there... the code is at <a href="http://www.khanacademy.org/cs/ode21/1077726566">http://www.khanacademy.org/cs/ode21/1077726566</a>
  • 4.
    nad
    edited October 2012

    meanwhile the students had a walk-up against ode-solvers:

    http://www.khanacademy.org/cs/ode22/1077647970

    Comment Source:meanwhile the students had a walk-up against ode-solvers: <a href="http://www.khanacademy.org/cs/ode22/1077647970">http://www.khanacademy.org/cs/ode22/1077647970</a>
  • 5.

    by the way I meanwhile saw that Mike Stay had posted a modified version.

    I placed the origin approximately at the origin of the Khan academy coordinate system (apart from a little offset to give a little space for the numbers), but thats may not where you wanted it to be ? By the way what exactly do you mean by Euler scheme ? The Euler method?

    Comment Source:by the way I meanwhile saw that Mike Stay had posted a modified version. I placed the origin approximately at the origin of the Khan academy coordinate system (apart from a little offset to give a little space for the numbers), but thats may not where you wanted it to be ? By the way what exactly do you mean by Euler scheme ? The Euler method?
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