FindFit for a differential equation model with multiple variables

*To*: mathgroup at smc.vnet.net*Subject*: [mg131630] FindFit for a differential equation model with multiple variables*From*: dantimatter <google at dantimatter.com>*Date*: Fri, 13 Sep 2013 00:36:55 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-outx@smc.vnet.net*Delivered-to*: mathgroup-newsendx@smc.vnet.net

Hello All I'm trying to figure out how to use FindFit with a multivariable differential equation model and data. I've successfully made it work for the one-variable version of the model by following the example on the Help page: %%%%%%%%%%%%%%%%%%% X_const = 10; model[a_?NumberQ, b_?NumberQ, c_?NumberQ, Km_?NumberQ, NTP0_?NumberQ] := (model[a, b, c, Km, NTP0] = First[MG /. NDSolve[{MG'[t] == a*X_const*NTP[t]/(Km + NTP[t]) - b MG[t], NTP'[t] == -a*X_const*NTP[t]/(Km + NTP[t]) - Exp[c] NTP[t], NTP[0] == NTP0, MG[0] == 0}, {MG, NTP}, {t, 0, 800}]]); fit = FindFit[data, model[a, b, c, Km, NTP0][t], {{a, 20}, {b, .017}, {c, -3}, {Km, 5000}, {NTP0, 15000}}, t] %%%%%%%%%%%%%%%%%%% where the data looks like: data = {{1.65, 111}, {4.65, 141}, {7.65, 130}, {10.65, 247}, {13.65, 301}, {16.65, 395}, {19.65, 444}, {22.65, 652}, ...}; But now I'd like to do it with 'X_const' being an additional variable included in the data like: newdata = {{1.65, 10, 111}, {4.65, 10, 141}, {7.65, 10, 130}, ..., {1.65, 5, -4}, {4.65, 5, 118}, {7.65, 5, 86}, {10.65, 5, 85}, {13.65, 5, 110}, ...}; I imagine that this is something that's possible, but I'm not sure on the syntax. Anyone have any thoughts on this? Many thanks!