NDSolve with a function which calls N

• To: mathgroup at smc.vnet.net
• Subject: [mg25459] NDSolve with a function which calls N
• From: Carl Woll <carlw at u.washington.edu>
• Date: Sun, 1 Oct 2000 02:44:43 -0400 (EDT)
• Sender: owner-wri-mathgroup at wolfram.com

I'm trying to use NDSolve with a rather complicated function, and with a
working precision greater than 16. Call the working precision I use
ndprec. In computing the complicated function, I need to temporarily set
the precision of some my arguments to a much higher value than the
working precision in NDSolve. When I try to use the function N within my
function with this higher precision, for example N[x,ndprec+10],
Mathematica complains that the precision I requested (ndprec+10) is
greater than \$MaxPrecision, where Mathematica's internal routines have
set \$MaxPrecision to ndprec.

To solve this problem, I tried to reset \$MaxPrecision to a higher value,
but Mathematica complains that \$MaxPrecision has been locked by internal
routines.

Below I present a simplified example to demonstrate the problem. Any
suggestions on how I can use N within the function a would be much
appreciated.

Carl

In[36]:=
Clear[a]
a[x_?NumericQ]:=Module[{},
N[\[Pi],30];
1]

In[38]:=
NDSolve[
{f'[x]+a[x]f[x]==1,f[0]==1/2},
f,
{x,0,1},
WorkingPrecision->24]

N::preclg:
Requested precision 30
is larger than \$MaxPrecision.
Using current \$MaxPrecision of 24
Infinity specifies that any
precision should be allowed.

N::preclg:
Requested precision 30
is larger than \$MaxPrecision.
Using current \$MaxPrecision of 24
Infinity specifies that any
precision should be allowed.

N::preclg:
Requested precision 30
is larger than \$MaxPrecision.
Using current \$MaxPrecision of 24
Infinity specifies that any
precision should be allowed.

General::stop:
Further output of N::preclg
will be suppressed during this
calculation.

Out[38]=
{{f -> InterpolatingFunction[{{0,

1.00000000000000000000000}},

<>]}}

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