Hello!

After using of-the-shelf ODE solvers and knowing how to use them, I now want to embed a solver in an application for users knowing nothing about ODEs. From real physics and engineering I know that numerical results need an error margin. If I fly somewhere (interplanetary), I would gladly accept doubled computation time if I know for sure that my probe reaches Mars. I am dreaming of using modern language features from C# or Java or C++11 or so to give an ODE solver more awareness about the problem. The user is supposed to enter a model much like in "the incredible machine", but may in later versions also enter text formulas. Keeping everything in objects, incorporating some simple algebra system, I should be able to go beyond Fortran inspired code! With car racing games or snooker I can estimate errors. But then 4d sports driving and Blender game engine break down occasionally.

Even for simpler problems, I read that I should use proven code. Maybe I can translate C code, but I have trouble finding anything. Since someone else pays for this and wants a return on investment, the code needs to be licensed under MIT or BSD license.

Not enough "coming of age": http://www.hindawi.com/journals/mpe/2012/565896/

Or not enough motivation for me? Why polynom, why Legendre? Dispersion?? Estimate? I want to be sure.

Writing fast programs makes more fun. I feel that I get a speed problem when the AI uses the simulation to optimize its behavior. Premature optimization and all that. The AI only wants the end result, not a fixed time step animation for display.

Off topic: Last posts: The web-project with authentication went to an expensive company with respective track record. With all other projects I use third party authentication.

Greetings
Arne

I tinkered around with this problem a bit and now think I use a trial function (polynom). I can easily take the derivative of a polynom. I then have to check that the user given function which relates by function to its derivate is within an error margin of my polynom. For this I need a library which can take derivatives of formulas for a taylor series or even some other stuff like transformations in orthogonal polynom bases (chebeychev, legendre, laguerre).

Thank you for the link. Bookmarked. It is sure better than trying to find zero points of a function. I could calculate derivatives to some order and calculate pessimistic bounds. That would allow me to modify the highest order term in a Taylor series to get bounds. Let's say I work with RK4, so everything is already precise to fourth order, I would have a x^5 divergence of my trust interval with time. Thank IEEE for 64 bit floating points (and Intel for 80 bit).

Pessimistic bounds: sine gives lower bound of -1 and upper of 1. Product gives upper bound of max*max and lower of min*min (add some cases for signs).

RK and Adam-Moulden assume that the trajectory is a polynom. Taylor is polynom. I can insert them, multiply them, subtract them. It sounds too good to be true. I certainly need some proofs of Weirstrass, Jacobi, Hilbert, orthonomality, idem potenz or the like.