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)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

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