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MathGroup Archive 2012

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NDSolve: Transmissive boundary conditions?

  • To: mathgroup at smc.vnet.net
  • Subject: [mg127795] NDSolve: Transmissive boundary conditions?
  • From: Mara Grahl <grahl at th.physik.uni-frankfurt.de>
  • Date: Thu, 23 Aug 2012 02:52:43 -0400 (EDT)
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Dear mathgroup,

say I have a second order partial differential equation. Therefore I
have to specify two boundary conditions. If I specify less, NDSolve
produces a warning like

NDSolve::bcart: Warning: An insufficient number of boundary conditions
have been specified for the direction of independent variable.
Artificial boundary effects may be present in the solution.

What boundary condition is used by Mathematica to obtain the solution in
such a case? I guess that transmissive (transparent) boundary conditions
are used, because I cannot think of something else. Is this true? So the
value for the function at the boundary without condition specified, is
simply set to the value of the function at the grid point next to it. Is
this what is done by Mathematica exactly, or is it more complicated?

Thank you, best regards,
Mara







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