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