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inequality as constraints on NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg106196] inequality as constraints on NDSolve
  • From: "Stefano Pasetto" <spasetto at ari.uni-heidelberg.de>
  • Date: Tue, 5 Jan 2010 01:42:24 -0500 (EST)

Dear Mathematica experts:

is there a possibility to implement a constraint in NDSolve?

Suppose I want to solve

 

NDSolve[{x'[t] == -y[t] - x[t]^2, y'[t] == 2 x[t] - y[t]^3,   x[0] == y[0]
== 1}, {x, y}, {t, 20}]

 

But I want that the solutions satisfied the inequality x[t]>0 for every t
(because it represent a physical quantity that has no meaning to be
negative), i.e., and when it becomes =0 it has to stay zero. I've tried
something like 

 

x[t_]:=If[x[t]>0,x[t],0]

 

in the definition of x or y but it does not make sense. Somehow, I'd need to
change the solution of the system when the solution itself become negative.

ThankX for the help, :-)

Best regards

Stefano Pasetto


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