MathGroup Archive 2008

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

Search the Archive

PDE with two variables by NDSolve

  • To: mathgroup at smc.vnet.net
  • Subject: [mg94500] PDE with two variables by NDSolve
  • From: "Alexei Boulbitch" <boulbitch at gmx.de>
  • Date: Mon, 15 Dec 2008 07:43:25 -0500 (EST)

Dear MathGroup members,

I have a misunderstanding when solving a partial differential equation with M6. It is a rather simple equation for a function z=z(x,y):

pde = \!\(
\*SubscriptBox[\(\[PartialD]\), \({x, 2}\)]\ \(z[x, y]\)\) + \!\(
\*SubscriptBox[\(\[PartialD]\), \({y, 2}\)]\ \(z[x, 
      y]\)\) - (1 - 3*Exp[-(x^2 + y^2)])*z[x, y] - 
    Log[(1 + z[x, y])/(1 - z[x, y])] == 0;

with simple boundary conditions fixed on a square 10x10. The function should be there either zero, or something small, but different from zero like 0.01. Let us take zero:

bc = {z[-10, y] == z[10, y] == 0, z[x, -10] == z[x, 10] == 0};

Now application of the NDSolve operator:

sol = NDSolve[{pde, bc}, z, {x, -10, 10}, {y, -10, 10}]

returns the error message:

NDSolve::ivone: Boundary values may only be specified for one \
independent variable. Initial values may only be specified at one \
value of the other independent variable. >>

I understand this response, as if Mathematica does not support boundary conditions fixed for both of the variables. 
However, in Help/NDSolve/ Scope/Partial Differential Equations/Example Nr 3 shows the following code for SineGordon:

L = 4;
sol = NDSolve[{D[u[t, x, y], t, t] == 
    D[u[t, x, y], x, x] + D[u[t, x, y], y, y] + Sin[u[t, x, y]], 
   u[t, -L, y] == u[t, L, y], u[t, x, -L] == u[t, x, L], 
   u[0, x, y] == Exp[-(x^2 + y^2)], 
   Derivative[1, 0, 0][u][0, x, y] == 0}, 
  u, {t, 0, L/2}, {x, -L, L}, {y, -L, L}]

in which the  line u[t, -L, y] == u[t, L, y], u[t, x, -L] == u[t, x, L] fixes very similar type of boundary conditions. 

What´s wrong?

Regards, Alexei
-- 
Alexei BOULBITCH,
Dr. , habil. 
IEE S.A.
Department for Material Development
ZAE Weiergewan
11, rue Edmond Reuter
L-5326 Contern, Luxembourg

Tel.          ++352-2454-2566
Fax.:        ++352 424737201
mobile:         0152-03807245
E-mail:      alexei.boulbitch at iee.lu
Internet:   http://www.physik.tu-muenchen.de/~aboulbit/

Psssst! Schon vom neuen GMX MultiMessenger gehört? Der kann`s mit allen: http://www.gmx.net/de/go/multimessenger


  • Prev by Date: Re: Small question about Filling between two functions in a
  • Next by Date: Re: Beginner: List Indexing and Assignment
  • Previous by thread: Re: Mathematica 7 Palettes Stays in front of notebook window,
  • Next by thread: Re: PDE with two variables by NDSolve