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MathGroup Archive 2006

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Re: NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg66009] Re: NDSolve
  • From: Jean-Marc Gulliet <jeanmarc.gulliet at gmail.com>
  • Date: Wed, 26 Apr 2006 04:38:26 -0400 (EDT)
  • Organization: The Open University, Milton Keynes, UK
  • References: <e2kq0u$77u$1@smc.vnet.net>
  • Sender: owner-wri-mathgroup at wolfram.com

Pat wrote:
> 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
> 
Hi Patrick,

First, use a single equal sign = to make a assignment to S. The double 
equal sign == tests the equality of two expressions.

Second, check the beginning of the following URL (also in the online 
help) to understand the use of replacement rules
http://documents.wolfram.com/mathematica/Built-inFunctions/NumericalComputation/EquationSolving/FurtherExamples/NDSolve.html

Third, as written and after correction of the assignment to S, your 
system produces many errors {division by zero, complex infinity 
encountered, ...)

Best regards,
Jean-Marc



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