Change ode23 to call oderkf

[acroy]

As discussed this changes ode23 to call oderkf with Bogacki–Shampine coefficients. The original ode23 is renamed to ode23_ncm (and moved to a separate file) for comparison and regression detection. README and LICENSE are updated.

[tomasaschan]

LGTM, although I'm not sure why we want to keep and export the old implementation - aren't we running the same tests on the new one as we did on the old one?

Btw, the Travis build failed once due to connectivity issues with Github, probably related to the ongoing DDoS attack against GH. I restarted it hoping for better luck this time.

[mauro3]

This paragraph seems wrong, no?

[acroy]

Yes, it is outdated. Part of #57 was about fixing this.

[acroy]

It's not exported. But I also don't mind to remove it.

I also had problems to push to my github repo. Let's hope they sort it out.

[coveralls]

Coverage remained the same at 95.09% when pulling fc9b436 on acroy:ode23ncm into 8701944 on JuliaLang:master.

[acroy]

Thanks to @tlycken's patch I hope that both Travis runs will pass now. The question remains if we want to keep the old ode23 or not?

[coveralls]

Coverage remained the same at 95.09% when pulling ae71674 on acroy:ode23ncm into 064a480 on JuliaLang:master.

[tomasaschan]

Is the new implementation independent enough that we can drop any possible licensing issues we had with the old one? (I seem to recall a discussion about MATLAB's license not being MIT-compatible...)

[acroy]

I don't know about the form of license of the old ode23 (in LICENSE.md it only says "Copyright 2012 Cleve Moler and The MathWorks, Inc."). Our oderkf probably counts as "derived work" from Octave's ode45, which is GPL. I think it wouldn't be difficult to reimplement it (say using Hairer's book), but obviously (?) I can't do that.
Forode23s I only used the paper of Shampine & Reichelt and I put it under MIT license, which is hopefully OK.

[mauro3]

I that case I'd say, better remove ode23. I made an explicit RK implementation following Hairer's book. Once I've cleaned it up, I'll post it, maybe it can replace oderkf.

[tomasaschan]

@mauro3 Nice!

@acroy To me it sounds like we don't need the old ode23 for anything anymore, so you can delete it if you like, or merge this PR as is and we'll delete it together with the current oderkf. I'm fine either way.

[acroy]

I removed ode23_ncm in the second commit.

@mauro3 : It would be great to have your RK implementation in ODE.jl. And it shouldn't be too hard to replace oderkf.

[coveralls]

Coverage increased (+0.59%) to 95.68% when pulling d1c0467 on acroy:ode23ncm into 064a480 on JuliaLang:master.

[ViralBShah]

I had taken ode23 was from Cleve Moler's textbook, and ode45 from octave originally. So the comments about the licenses of both are spot on.

Perhaps it is best to remove ode23, and while GPL is perfectly fine, a non-GPL ode solver if @mauro3 has one, is also nice to have.

[tomasaschan]

@acroy Are you waiting for something specific to merge this?

[acroy]

No, it was just Easter dementia :-)