Services & Resources / Wolfram Forums
-----
 /
MathGroup Archive
1995
*January
*February
*March
*April
*May
*June
*July
*August
*September
*October
*November
*December
*Archive Index
*Ask about this page
*Print this page
*Give us feedback
*Sign up for the Wolfram Insider

MathGroup Archive 1995

[Date Index] [Thread Index] [Author Index]

Search the Archive

Re: Help with NDSolve

  • To: mathgroup at christensen.cybernetics.net
  • Subject: [mg1541] Re: Help with NDSolve
  • From: rknapp (Robert Knapp)
  • Date: Sat, 24 Jun 1995 02:37:25 -0400
  • Organization: The Santa Fe Institute

In article <3s86l4$och at news0.cybernetics.net> imm at cs.umd.edu (Ibrahim Matta) writes:

> I am trying to solve a differential equation 
>   NN'[t] = lambda ( 1 - B[t] ) - mu NN[t]
> where B[t] is a fixed point of a function of NN[t] and B[t].
> 
> The program below does not, however, terminate.
> It works if we use Nest instead of FixedPoint, but
> we need FixedPoint for the stopping criteria.
> I suspect that with FixedPoint Mathematica can not
> symbolically get the differential equations.
> Is there a way around this or it can't be done with
> Mathematica ?
> 
> Any help is very much appreciated.
> 
> Best regards,
> Ibrahim
> 
> =============================================
> 
> T = 20
> lambda = 0.8 
> mu = 1.0
> K = 2
> 
> Clear[NN]
> Clear[B]
> 
> 
> B[b_] := (NN[t] / (1 - b))^K / K! / 
>                         (1 + Sum[(NN[t] / (1 - b))^ii / ii!, {ii, K}])
> 
> 
> 
> 
>  sol = NDSolve[{NN'[t] == 
>         lambda (1 - FixedPoint[B, 0.1, SameTest->(Abs[#1 - #2] < 10.^-4 &)]) 
>         - mu NN[t], NN[0] == 0}, 
>                 NN, {t, T}]
> 
> Plot[Evaluate[NN[t] /. sol], {t, 0, T}]
> 
> =============================================

Your problem here is that NDSolve evaluates the equation before solving the equations.  You will find that if you simply evaluate

{NN'[t] == 
         lambda (1 - FixedPoint[B, 0.1, SameTest->(Abs[#1 - #2] < 10.^-4 &)]) 
         - mu NN[t], NN[0] == 0}

by itself, the FixedPoint does not terminate because the condition is
never met with a symbolic N[t].

The solution (generally a good one in any case like this where
non-numeric evaluation is dangerous) is to prevent symbolic
evaluation.  Here is a fix:

define a new function:

FixPointB[val_?NumberQ] :=
	FixedPoint[B[val], 0.1, SameTest->(Abs[#1 - #2] < 10.^-4 &)]

this tests the argument "val" to be sure that it is a number before
attempting FixedPoint.  Using this function and your other
definitions, the call to NDSolve:


In[17]:=
sol = NDSolve[{NN'[t] == 
        lambda (1 - FixPointB[NN[t]]) 
        - mu NN[t], NN[0] == 0}, 
                NN, {t, T}]
Out[17]=
{{NN -> InterpolatingFunction[{0., 20.}, <>]}}

works as it should.


Rob Knapp
WRI




  • Prev by Date: Implicit surface plotting
  • Next by Date: Re: counting number of rules in rule base
  • Previous by thread: Re: counting number of rules in rule base
  • Next by thread: Help with NDSolve