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MathGroup Archive 2009

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Functions in partial differential equations with different number of

  • To: mathgroup at smc.vnet.net
  • Subject: [mg99470] Functions in partial differential equations with different number of
  • From: Blue Fly <blueflyspin at gmail.com>
  • Date: Wed, 6 May 2009 05:25:37 -0400 (EDT)

Hi, I was trying to solve the following set of PDE:
s=0.01;
NDSolve[{-I*D[R[x,t],x] + (s/(Pi (x^2+ s^2)))*F[t] ==I*D[R[x,t],t], 2 F[t] +
R[0,t]== I*D[F[t],t], R[-20, t]==R[20,t], R[x,0]==Exp[-(x+5)^2],
F[0]==0},{R, F}, {x,-20, 20}, {t, 0,10}]

where I is the imaginary number Sqrt[-1].

However, Mathematica gave an error message saying that A and F have
different number of dependent variables:
"NDSolve::"dvlen" :  "The function F[t] does not have the same number of
arguments as independent variables (2)."

This set of equations simulate a one-dimensional wave hits a localized
target at x=0 (approximates using a Lorentzian). Initial wave form at t=0 is
given by R[x, 0]. The computation domain in x is assumed to be periodic.

Thank you for any help and suggestions.

Dave



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