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Re: A NDSolve within a FindMinimum/NMinimize

  • To: mathgroup at smc.vnet.net
  • Subject: [mg90606] Re: A NDSolve within a FindMinimum/NMinimize
  • From: dh <dh at metrohm.ch>
  • Date: Tue, 15 Jul 2008 06:49:49 -0400 (EDT)
  • References: <g5htfb$j7t$1@smc.vnet.net>




Hi Philipp,

you have 2 bugs here. First, NMinimize first calls the function with a 

symbolic argument to see if it can do a symbolic simplification. You may 

fix this by wrapping a function with a numerical argument around your code.

Second, NMinimize returns a list of results, even if there is only one 

result. To fix this, you simply take the first element of the list. Here 

is the corrected code:

f[a_?NumericQ]:=(s=NDSolve[{El'[x]+a Sin[x] 

El[x]==0,El[0]==a},El,{x,-1,1}][[1]];(El[1]/.s) a)

NMinimize[f[a],a]

hope this helps, Daniel





philip.ingrey at googlemail.com wrote:

> I'm trying to find the value of a coefficient that minimizes a

> function. Below is a simplified version of the problem:

> Using a Table to print out some results is fine:

> 

> Table[{a, s = NDSolve[{El'[x] + a Sin[x] El[x] == 0, El[0] == a}, El,

> {x, -1, 1}]; ((El[1] /. s) a)[[1]]}, {a, -1, 1, 0.1}]

> 

> But a NMinimize or FindMinimum gives errors:

> 

> NMinimize[s = NDSolve[{El'[x] + a Sin[x] El[x] == 0, El[0] == a}, El,

> {x, -1, 1}]; (El[1]  /. s) a, a]

> 

> As it seams to try and evaluate the NDSolve then apply a value for a,

> is there a way to solve this?

> 

> Thanks in advance,

> Phil I

> 





-- 



Daniel Huber

Metrohm Ltd.

Oberdorfstr. 68

CH-9100 Herisau

Tel. +41 71 353 8585, Fax +41 71 353 8907

E-Mail:<mailto:dh at metrohm.com>

Internet:<http://www.metrohm.com>




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