search

numerical-mooc / assignment-bank

Contribute alternative assignments for Numerical Methods with Python
MIT License
14 stars 75 forks source link

a notebook to illustrate the weird things that the leap frog method can do, at times. #5

Closed ghost closed 10 years ago

IanHawke commented 10 years ago

There's an issue with the PR that it won't automatically merge; could you close, update your repo and recreate?

Comments here are based on a straight clone of your repository.

I mostly like this a lot. I have one language/conceptual issue with the pay-off line - that leapfrog is "solving the wrong equations". I would disagree with that, as I would interpret that statement to precisely mean that leapfrog is inconsistent with the IVP, ie that the truncation error does not tend to zero with resolution.

The phrasing that I prefer is that the discrete equations admit multiple solutions (always true), and that leapfrog does not ensure that the contribution of the "wrong" solutions is either small, or tends to zero with resolution (which eg midpoint rule does). I don't have a snappy way of phrasing this.

gforsyth commented 10 years ago

Merging issue is due to how we split leapfrog notebook off of the first pull request. I will resolve the conflict when the notebook is ready to go On Sep 25, 2014 6:39 PM, "Ian Hawke" notifications@github.com wrote:

There's an issue with the PR that it won't automatically merge; could you close, update your repo and recreate?

Comments here are based on a straight clone of your repository.

I mostly like this a lot. I have one language/conceptual issue with the pay-off line - that leapfrog is "solving the wrong equations". I would disagree with that, as I would interpret that statement to precisely mean that leapfrog is inconsistent with the IVP, ie that the truncation error does not tend to zero with resolution.

The phrasing that I prefer is that the discrete equations admit multiple solutions (always true), and that leapfrog does not ensure that the contribution of the "wrong" solutions is either small, or tends to zero with resolution (which eg midpoint rule does). I don't have a snappy way of phrasing this.

— Reply to this email directly or view it on GitHub https://github.com/numerical-mooc/assignment-bank/pull/5#issuecomment-56894664 .

ghost commented 10 years ago

I'll try to redo this pull request