Trouble solving system of first order, two variable PDEs in

*To*: mathgroup at smc.vnet.net*Subject*: [mg93341] Trouble solving system of first order, two variable PDEs in*From*: Tim Mc <tmccomb at creol.ucf.edu>*Date*: Tue, 4 Nov 2008 06:18:52 -0500 (EST)

Hello All, I am trying to solve what will become a large system of PDEs (20-30 equations) (though now it is only three representative equations) using the Mathematica NDSolve function. The equations all only involve first derivatives and are a function of one time and one space variable. I have inserted the code below. When I attempt to evaluate I get the error: 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 It seems no matter what I do (even stripping off the numbers and breaking the equations down to their bare bones) I always get this error for these type of boundary conditions. Can any one give me any advice on whether I am doing something wrong in the software or if my set of equations are simply incorrectly posed? This is my Mathematica code: \[Sigma]es = 3.4*^25; \[Sigma]as = 5*^-27; \[Sigma]ep = 5*^-26; \[Sigma]ap = 8*^-25; \[Tau] = 840*^-6; \[Alpha] = 3*^-3; Nn = 6*^25; \[CapitalGamma] = 0.85; \[CapitalGamma]p = 0.01; \[Lambda]p = 0.915*^-6; \[Lambda]s = 1.064*^-6; A = 3*^-10; h = 6.626*^-34; c = 3*^8; n = 1.5; eq1 = D[N2[z, t], t] == (\[CapitalGamma]p*\[Lambda]p/(h*c*A)) (\[Sigma]ap*(Nn - N2[z, t]))*Pp[z, t] - N2[z, t]/\[Tau] + (\[CapitalGamma]*\[Lambda]s/(h*c* A)) (\[Sigma]as*(Nn - N2[z, t]) - \[Sigma]es*N2[z, t])* Pp[z, t]; eq2 = D[Pp[z, t], z] + (n/c)* D[Pp[z, t], z] == -\[CapitalGamma]p (\[Sigma]ap*(Nn - N2[z, t]) - \[Sigma]ep*N2[z, t])*Pp[z, t] - \[Alpha]* Pp[z, t]; eq3 = D[Ps[z, t], z] + (n/c)* D[Ps[z, t], z] == \[CapitalGamma] (\[Sigma]es* N2[z, t] - \[Sigma]as*(Nn - N2[z, t]))*Ps[z, t] - \[Alpha]* Ps[z, t]; bc1 = Ps[0, t] == 1; bc2 = Pp[0, t] == 20; bc3 = N2[z, 0] == 0; solution = {N2, Pp, Ps} /. First[NDSolve[{eq1, eq2, eq3, bc1, bc2, bc3}, {N2, Pp, Ps}, {z, 0, 10}, {t, 0, 0.001}]] The error I see: 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. >> Thank You in Advance, Tim