Services & ResourcesWolfram ForumsMathGroup Archive

[Date Index] [Thread Index] [Author Index]

Problem with NDSolve in Mathematica V4

• To: mathgroup at smc.vnet.net
• Subject: [mg103337] Problem with NDSolve in Mathematica V4
• From: "thfrommelt at web.de" <thfrommelt at web.de>
• Date: Wed, 16 Sep 2009 05:46:42 -0400 (EDT)

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

• Follow-Ups:
  • Re: Problem with NDSolve in Mathematica V4
    • From: DrMajorBob <btreat1@austin.rr.com>