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Would an ODE solver written in C perhaps using the GSL library have significant speed advantages compared with Mathematica 8.0 NDSolve? How would it fair in terms of accuracy?

My understanding is that compiled code could in principle be faster, but that these days NDSolve uses a lot of compiled code itself already somehow?

Also are there any options for using things like MathLink or Mathematica's compile function to speed solving an ODE up?

fpghost
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  • by the way, if you are concern with performance, try c++ odeint. that's what i'm using. it has more modern integrators and better performance – kirill_igum Nov 05 '12 at 19:24

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NDSolve and other numerical functions in Mathematica automatically compile your operand (e.g. the RHS of an ODE) to an intermediate "bytecode" language (the same one used by the Compile function). If you like you can specify CompilationTarget -> "C" and the function will be compiled all the way to C code and linked back in to Mathematica... You can see the generated C code yourself in this previous question on the Mathematica Stack Exchange:

https://mathematica.stackexchange.com/questions/821/how-well-does-mathematica-code-exported-to-c-compare-to-code-directly-written-fo/830#830

Of course, it's always possible in principle to hand-write a faster algorithm... But there are a lot of things to optimize that Mathematica will do automatically. You probably don't want to be responsible for manually optimizing the computation of a sparse matrix of partial derivatives in an optimization problem for example.

Community
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Andrew Moylan
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Mathematica's focus is on usability. They do use numerical libraries. So the speed would be the same as the best available library or worse (in almost all cases). for example, i heard they use eigen for matrix stuff.

the other thing that you should consider is that although they optimize functions that they provide, your own functions are not optimized. so the derivative that you calculate at each step would be faster in c.

to my friends that decide between mathematica and c++, i tell to go with mathematica since they should focus on getting results fast rather than building the fastest code.

kirill_igum
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  • "although they optimize functions that they provide, your own functions are not optimized" Is there a way to use Mathematica's Compile to avoid this pitfall and thus equal the c speed? – fpghost Oct 18 '12 at 20:40
  • not mathematica compile but you can make mathematica interface with c libs. so you should make your function as c lib. if you know or would learn how to do that, it would be easier to just use c. – kirill_igum Oct 18 '12 at 21:48
  • by the way, i found http://www.nongnu.org/gsl-shell/ is pretty good for prototyping. it's fast and easy. – kirill_igum Oct 18 '12 at 21:49