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