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MathGroup Archive 2006

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NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg65968] NDSolve
  • From: "Pat" <patrick.wikus at cern.ch>
  • Date: Tue, 25 Apr 2006 05:18:37 -0400 (EDT)
  • Sender: owner-wri-mathgroup at wolfram.com

Hi,

I have a problem with Mathematica. I am trying to solve a partial
differential equation but do not suceed in obtaining a result.
First, I define a polynomial function S which depends on x and t:

S == 10.084304421395792 + 114.57416854230641*t +
115.11466668494609*(t^2) - 3822.35951791628*(t^3) +
23192.835807699386*(t^4) - 77725.26066741263*(t^5) +
161907.74898800353*(t^6) - 213918.36222839082*(t^7) +
174300.72308993243*(t^8) - 79865.31220440594*(t^9) +
15736.460820905904*(t^10)- 205.6915345278371*x-
1009.7681219413579*(x^2) + 21511.565356040668*(x^3) +
320164.63081689784*(x^4)- 494743.9951075827*(x^5) -
6.506685473054829*(x^6) -
6.902121854594892*(x^7) + 5.981554201963775*(x^8) +
2.269398919104073*(x^9) - 1.9233253999085125*(x^10)

I then want to calculate the function Q(x,t) as follows:

NDSolve[{Q[x, t] == -t*(x^2)*(D[S, x] + D[S, t]*(-D[Q[x, t], x]/D[Q[x,
t], t])), Q[0, t] == 0}, Q[x, t], {t, 0.001, 1}, {x, 0.03, 0.06}]

and Mathematica yields a result by outputting

{{Q[x, t] -> InterpolatingFunction[{{0.001, 1.}, {0.03, 0.06}}, <>][t,
x]}}

If I try to obtain numerical values from that object, no useful result
is obtained.If I query Q[0.04, 0.04], for instance, the result is just
the same Q[0.04, 0.04], but no value.

Do you have an idea how this could work?

Cheers,
Patrick


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