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how to solve a ode systems of size of four?

asked 2011-10-02 14:26:38 +0100

Nan gravatar image

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)


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

Thanks for answering.

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answered 2011-10-03 04:47:27 +0100

Nan gravatar image

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

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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 gravatar imageDSM ( 2011-10-03 10:10:52 +0100 )edit

answered 2011-10-03 04:44:21 +0100

Nan gravatar image

updated 2011-10-04 08:10:56 +0100

Jason Grout gravatar image

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
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answered 2011-10-02 16:39:42 +0100

DSM gravatar image

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 "....:".]

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Asked: 2011-10-02 14:26:38 +0100

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Last updated: Oct 04 '11