MaplePrimes - answers and comments on Question, Finding all roots for an ODE in a given interval

Try avoid (one way)

Kamel Boughrara — Tue, 19 Jul 2011 22:26:30 Z

fsolve((rhs(ODE_4))(t)=0,t, avoid={t10},10..20); # t10 is the solution that you find at the first

Try also to serch complex solution with adding option complex

See

?fsolve/details

Use it as a component

epostma — Tue, 19 Jul 2011 23:19:00 Z

@vicaut : You can use Kamel's idea as a component to building a solution that includes all the roots. In fact, I would suggest using the ?RootFinding/NextZero command; it has somewhat better numerical behaviour and its behaviour is a bit better specified than fsolve for this type of question (where you want to "avoid" many roots). Define the following (Maple 15) procedure:

allRoots := proc(f :: procedure, rng :: range, $)
local result, root;
  result := Vector(0, 'datatype = float');
  root := RootFinding:-NextZero(f, lhs(rng), 'maxdistance' = rhs(rng) - lhs(rng));
  while root <> FAIL and root <= rhs(rng) do
    result(numelems(result) + 1) := root;
    root := RootFinding:-NextZero(f, root, 'maxdistance' = rhs(rng) - root);
  end do;
  return result;
end proc;

Now allRoots(rhs(ODE_4), 10 .. 20) should give you a Vector with all the (100 or so) roots that you were talking about.

Hope this helps,

Erik Postma
Maplesoft.

There was a very interesting discussion on

longrob — Tue, 19 Jul 2011 23:31:22 Z

There was a very interesting discussion on this topic, which included the method shown by epostma above, recently here:

http://www.mapleprimes.com/questions/123476-Seeking-A-Good-Praxis-In-Solving-Equations

Thats not what i mean. I'm not interested

vicaut — Tue, 19 Jul 2011 22:38:55 Z

Thats not what i mean. I'm not interested in the complex roots, but i need some kind of procedure that lists all the roots in the interval AT ONCE. I can't repeat the input with avoid, i have about 100 or more roots in this interval!

Worked quite well in Maple 15.00 but not in 15.01.

vicaut — Thu, 28 Jul 2011 00:55:34 Z

After updatig, this procedure is awfully slow. "allRoots(rhs(ODE_4),50..50.1)" needs more than a minute to get the one and only root in this interval! And i need 500 computations with different numbers for a parameter in my ODE and a range from 100 to 150 or even higher to get a plot with all the roots dependant on the parameter. This computation would last days or weeks. Are there options to make this faster? I think there is a much faster option: I consider to find the roots with the "events=[y(t),...]" and maybe the eventfired option within my definition of my ODE, but i don't know how to get/save all the triggered events (= roots) to a vector, like in your procedure. Maple help for /dsolve/numeric/Events is not very helpful for me, because there aren't many examples/descriptions how to do this. Do you have any suggestions?