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Accurate PDE solution

  • To: mathgroup at smc.vnet.net
  • Subject: [mg128715] Accurate PDE solution
  • From: Leslaw Bieniasz <nbbienia at cyf-kr.edu.pl>
  • Date: Mon, 19 Nov 2012 19:17:39 -0500 (EST)
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Hi,

I need to solve a certain relatively simple PDE 
(evolutionary convection-diffusion in one space dimension)
but the problem is that I need a very accurate solution.
Ideally I would like to have 20 significant digits,
less ideally 16 digits, and in the worst case 10-12.
Are there any freely available procedures for MATHEMATICA
that can do this job? I presume some sort of adaptive solvers
would be needed. I notice that NDSolve can realistically provide
no more than 4 significant digits, even if one plays with
AccuracyGoal and PrecisionGoal parameters, which do not seem
to have much effect on the number of digits obtained.
What is worse, if one selects too many spatial nodes,
to satisfy these error tolerances, the program crashes
due to insuffucient memory.

Leslaw



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