Re: Problem with NDSolve in Mathematica V4
- To: mathgroup at smc.vnet.net
- Subject: [mg103362] Re: [mg103337] Problem with NDSolve in Mathematica V4
- From: DrMajorBob <btreat1 at austin.rr.com>
- Date: Thu, 17 Sep 2009 06:21:22 -0400 (EDT)
- References: <200909160946.FAA12995@smc.vnet.net>
- Reply-to: drmajorbob at yahoo.com
It looks good (a smooth U-shaped curve) in version 7.
Bobby
On Wed, 16 Sep 2009 04:46:42 -0500, thfrommelt at web.de <thfrommelt at web.de>
wrote:
> I experienced some difficulties with solving a 1D thermal conduction
> problem with my old Mathematica (V4 for Students):
> - spec. heat 1094J/kgK, density 354kg/m, thermal conductivity 0.05 W/
> mK
> - domain length: 2mm
> - Dirichlet boundary condition: temperature at both ends is risen at a
> heating rate of 10K/min starting with room temperature
> - Starting condition: Room temperature 293.15K in the whole domain
>
> I used the following command:
>
> solution =
> NDSolve[{1094*354*D[T[x, t], t] == 0.05 D[T[x, t], x, x],
> T[x, 0] == 293.15,
> T[0, t] == 293.15 + 10/60*t,
> T[2 10^-3, t] == 293.15 + 10/60*t},
> T, {x, 0, 2 10^-3}, {t, 0, 1980}, StartingStepSize -> {0.00001,
> 0.01}]
>
> A plot after 10 sek with
> Plot[T[x, 10] /. solution, {x, 0, 2 10^-3}, PlotPoints -> 20,
> PlotRange -> All]
>
> produces nonsense (see picture at
> http://www.thomas-frommelt.de/images/26910_WLF.jpg).
> Boundary conditions are obviously respected but the thermal conduction
> close to the right boundary is invalid.
>
> Meanwhile, I know that this error does not occur in Mathematica V6. I
> tried several options to achieve a correct solution in V4 as well:
> DifferenceOrder, MaxStepSize, AccuracyGoal, MaxSteps, WorkingPrecision
> - always the same result. Has anyone an idea?
>
> Thanks in advance
>
> Thomas
>
--
DrMajorBob at yahoo.com
- References:
- Problem with NDSolve in Mathematica V4
- From: "thfrommelt@web.de" <thfrommelt@web.de>
- Problem with NDSolve in Mathematica V4