how to solve a ode systems of size of four?

asked 2011-10-02 14:26:38 +0200

Nan
1

I want to solve the chemistry reaction rate. Here I got the 4 differential equatiobs.

dE/dt=-k1ES+k2ES+kiES dES/dt=k1ES-kiES-k2ES dS/dt=-k1ES+kiES dP/dt=k2ES

Here is my code?

k1,k2,ki,t=var('k1 k2 ki t') E=function('E',t) ES=function('ES',t) S=function('S',t) P=function('P',t)

des=(diff(E,t)==-k1ES+k2ES+kiES,diff(ES,t)==k1ES-kiES-k2ES diff(S,t)==-k1ES+kiES diff(P,t)==k2ES)

desolve_system(des,[E,ES,S,P],ivar=t,ics=[0,1,1,1,1])

The above is my code. But I just cannot execute it. I am a rookie with this kind of coding style.

Thanks for answering.

edit retag flag offensive close merge delete

add a comment

3 Answers

Sort by » oldest newest most voted

answered 2011-10-03 04:47:27 +0200

Nan
1

oh,this page cannot be post the symbol like the star which means multiplication...

edit flag offensive delete link

Comments

In order to get code formatted correctly, select some code and then hit the little button above the text box which reads "101010". It should show up in the preview box like mine did (note that I used the *.) But we still need to see the error message to figure out what's going wrong. Could you post that?

DSM ( 2011-10-03 10:10:52 +0200 )edit

add a comment

answered 2011-10-03 04:44:21 +0200

Nan
1

updated 2011-10-04 08:10:56 +0200

Jason Grout
3505 ●9 ●36 ●81

the four ode should be:

sage: de1=diff(E,t)==-k1*E*S+k2*ES+ki*ES
sage: de2=diff(ES,t)==k1*E*S-ki*ES-k2*ES
sage: de3=diff(S,t)==-k1*E*S+ki*ES
sage: de4=diff(P,t)==k2*ES

edit flag offensive delete link

add a comment

answered 2011-10-02 16:39:42 +0200

DSM

5242 ●21 ●68 ●112

Hi! "But I just cannot execute it" isn't very specific-- could you cut and paste the error message? Your code seems to work for me:

sage: k1,k2,ki,t=var('k1 k2 ki t') 
sage: E=function('E',t)
sage: ES=function('ES',t)
sage: S=function('S',t) 
sage: P=function('P',t)
sage: des=(diff(E,t)==-k1*ES+k2*ES+ki*ES,
....:      diff(ES,t)==k1*ES-ki*ES-k2*ES,
....:      diff(S,t)==-k1*ES+ki*ES, diff(P,t)==k2*ES)
sage: desolve_system(des, [E, ES, S, P], ivar=t, ics=[0,1,1,1,1])
[E(t) == -e^((k1 - k2 - ki)*t) + 2, ES(t) == e^((k1 - k2 - ki)*t), S(t) == -(k1 - ki)*e^((k1 - k2 - ki)*t)/(k1 - k2 - ki) + (2*k1 - k2 - 2*ki)/(k1 - k2 - ki), P(t) == k2*e^((k1 - k2 - ki)*t)/(k1 - k2 - ki) + (k1 - 2*k2 - ki)/(k1 - k2 - ki)]

although I did have to insert some commas which seemed missing from your des line. [Note that the above is a cut-and-paste from the console; you wouldn't actually enter "sage:" or "....:".]

edit flag offensive delete link

add a comment

Your Answer

Please start posting anonymously - your entry will be published after you log in or create a new account.

Add Answer

how to solve a ode systems of size of four?

3 Answers

Comments

Your Answer

Question Tools

Stats

Related questions

how to solve a ode systems of size of four? edit

3 Answers

Comments

Your Answer

Question Tools

Stats

Related questions

how to solve a ode systems of size of four?