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--

```

• Prev by Date: Plot3D precision limits?
• Next by Date: Re: Use a nicer Format for differences
• Previous by thread: Plot3D precision limits?
• Next by thread: Re: coupled ODE system: won't solve [?]