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Nonlinear fit to diff eqs.

• To: mathgroup at smc.vnet.net
• Subject: [mg4973] Nonlinear fit to diff eqs.
• From: mod <c530789 at showme.missouri.edu>
• Date: Thu, 17 Oct 1996 00:40:53 -0400
• Sender: owner-wri-mathgroup at wolfram.com

Dear All,

My problem is to fit a set of data to a system of coupled first order
ordinary differential equations. The example is:

   Experimental data of y1, y2 and y3 as a function of time
             y1 = {a1,a2,a3,a4,.....,aN}
             y2 = {b1,b2,b3,b4,.....,bN}
             y3 = {c1,c2,c3,c4,.....,cN}
             time = {t1,t2,t3,t4,.....,tN}
             
    Equations to fit (for example):

             y1'[t] = k1 y1[t] + k2 (1-y1[t]-y2[t]) + k4 y3[t]
             y2'[t] = k2 y2[t] - k3 (1-y2[t]) + k4 y3[t]
             y3'[t] = k3 (1-y1[t]-y2[t]-y3[t]) +k2 y3[t] 

I need to fit my data to get those k1, k2, k3, and k4. What is the easiest
to to do this with Mathematica? Any package? Please help.

Thaks in advance,

SF