Mathematica NDSolve max number of grid points error

• To: mathgroup at smc.vnet.net
• Subject: [mg22934] Mathematica NDSolve max number of grid points error
• From: Scott Beckman <sbeckman at uclink.berkeley.edu>
• Date: Thu, 6 Apr 2000 02:04:51 -0400 (EDT)
• Organization: University of California at Berkeley
• Sender: owner-wri-mathgroup at wolfram.com

```Hello,

I'm trying to solve a simple PDE with Mathematica's NDSolve function,
but I'm getting the error "Using maximum number of grid points 1500
allowed by the MaxSteps option.".  I've used the MaxSteps function to
increase the number of steps up to the point that I've consumed all the
available memory.  This isn't the right way to solve the problem.

Has anyone else had this problem and is there a way around it?  Are
there books on using Mathematica for numerical problems such as this?

Below are the lines I'm having problems with.  Its a simple little
program to calculate the heat conduction in x and t for one fixed T
boundary condition and one insulated boundary condition and an initial
temperature distribution that is constant.

>alpha = 1.32*10^-5

>solution =
NDSolve[{D[u[x, t], t] == alpha D[u[x, t], {x, 2}],
u[x, 0] == (UnitStep[(x - 0.000000001)]*(423 - 455) +
455), ((D[u[x, t], x]) /. x -> 0.00005) == 0, u[0, t] ==
455},
u, {x, 0, 0.00005}, {t, 0, 0.00003}, MaxSteps -> 1500];

>interf[tt_] := Evaluate[u[0.00005, tt] /. Last[solution]]

>FindRoot[interf[tim] == 428, {tim, 0.00001}]

Thanks for taking a look at this,
Scott

====================================================
Scott Beckman

University of California at Berkeley
Material Science and Mineral Engineering Department
577 Evans Hall #1760
Berkeley, CA  94720-1760