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MathGroup Archive 1997

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coupled ODE system: won't solve [?]

  • To: mathgroup at smc.vnet.net
  • Subject: [mg6503] coupled ODE system: won't solve [?]
  • From: Patrick Jemmer <padz at joule.pcl.ox.ac.uk>
  • Date: Thu, 27 Mar 1997 02:42:42 -0500 (EST)
  • Sender: owner-wri-mathgroup at wolfram.com

Hello all:

I was wondering if anyone might be able to help
me with my attempts to get MMA to solve the attacked set
of ODEs...

There are 8 equations, 1 for each unknown...

Am I simply hitting the ceiling in the complexity of such
systems MMA can handle ?

Cheers for any assistance.

Patrick.

--------------------------------------------------------------
| Dr Patrick Jemmer,      | http://berne.pcl.ox.ac.uk/~padz  |
| Physical & Theoretical  | e-mail: padz at joule.pcl.ox.ac.uk  |
| Chemistry Laboratory,   | tel: +44-1865-2-75161 (work)     | 
| South Parks Road,       | fax: +44-1865-2-75410            | 
| Oxford OX1 3QZ          | http://joule.pcl.ox.ac.uk/ (PTCL)|
--------------------------------------------------------------
DSolve[

{Derivative[1][En][t] == 
     km4*EI[t] - k3*En[t] + km1*ES[t] + km3*Inh[t] - k4*En[t]*Inh[t] - 
      km2*En[t]*P[t] - k1*En[t]*S[t], 

Derivative[1][S][t] == km1*ES[t] + k6*PI[t] - k1*En[t]*S[t] - 
      km6*Inh[t]*S[t],

Derivative[1][ES][t] == 
     -(k2*ES[t]) - km1*ES[t] + km2*En[t]*P[t] + k1*En[t]*S[t], 

Derivative[1][P][t] == k2*ES[t] - k7*P[t] - km2*En[t]*P[t] - 
      k5*Inh[t]*P[t] + km5*PI[t] + km7*T[t], 

Derivative[1][Inh][t] == km4*EI[t] + k3*En[t] - km3*Inh[t] - 
      k4*En[t]*Inh[t] - k5*Inh[t]*P[t] + k6*PI[t] + km5*PI[t] - 
      km6*Inh[t]*S[t],

Derivative[1][EI][t] == 
     -(km4*EI[t]) + k4*En[t]*Inh[t], 

Derivative[1][PI][t] == k5*Inh[t]*P[t] - k6*PI[t] - km5*PI[t] + 
      km6*Inh[t]*S[t],

Derivative[1][T][t] == k7*P[t] - km7*T[t], 

En[0] == 1, S[0] == 4, ES[0] == 0, P[0] == 0, Inh[0] == 0, EI[0] == 0, 
PI[0] == 0, T[0] == 1},

{En[t], S[t], ES[t], P[t], Inh[t], EI[t], PI[t], T[t]},

t]

--------------167E2781446B
Content-Disposition: inline; filename="math.mma"

DSolve[

{Derivative[1][En][t] == 
     km4*EI[t] - k3*En[t] + km1*ES[t] + km3*Inh[t] - k4*En[t]*Inh[t] - 
      km2*En[t]*P[t] - k1*En[t]*S[t], 

Derivative[1][S][t] == km1*ES[t] + k6*PI[t] - k1*En[t]*S[t] - 
      km6*Inh[t]*S[t],

Derivative[1][ES][t] == 
     -(k2*ES[t]) - km1*ES[t] + km2*En[t]*P[t] + k1*En[t]*S[t], 

Derivative[1][P][t] == k2*ES[t] - k7*P[t] - km2*En[t]*P[t] - 
      k5*Inh[t]*P[t] + km5*PI[t] + km7*T[t], 

Derivative[1][Inh][t] == km4*EI[t] + k3*En[t] - km3*Inh[t] - 
      k4*En[t]*Inh[t] - k5*Inh[t]*P[t] + k6*PI[t] + km5*PI[t] - 
      km6*Inh[t]*S[t],

Derivative[1][EI][t] == 
     -(km4*EI[t]) + k4*En[t]*Inh[t], 

Derivative[1][PI][t] == k5*Inh[t]*P[t] - k6*PI[t] - km5*PI[t] + 
      km6*Inh[t]*S[t],

Derivative[1][T][t] == k7*P[t] - km7*T[t], 

En[0] == 1, S[0] == 4, ES[0] == 0, P[0] == 0, Inh[0] == 0, EI[0] == 0, 
PI[0] == 0, T[0] == 1},

{En[t], S[t], ES[t], P[t], Inh[t], EI[t], PI[t], T[t]},

t]

--------------167E2781446B--


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