Solving 3 simultaneous first order differential equations
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Abhivyakti
le 29 Déc 2013
Commenté : Walter Roberson
le 29 Déc 2013
I need to solve the following set of differential equations using MATLAB.
Here, um,Ks,Kp,a,sm,yxs,K1,K2-constant values s,p,x- variables
I am using the function ode45 for this. This is my program :
function dydt=react(t,y)
dydt=zeros(3,1);
um=0.71;
ks=37.72;
sm=510;
kp=160.83;
a=0.81;
yxs=0.03;
ms=0.0011;
k1=33.04;
k2=0.0001;
y=zeros(3,1);
x=y(1);
s=y(2);
p=y(3);
dx=(um*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)))*x;
ds=-1*((um/yxs)*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)) + ms)*x;
dp=(k1*(um*(s/(s+ks))*((1-(s/sm))^a)*(kp/(kp+p)))+k2)*x;
dydt=[dx;ds;dp];
On giving this command :
[T,Y]=ode45('react',[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[0.2 100 0.2]);
or this command :
[T,Y]=ode45('react',[0 15],[0.2 100 0.2]);
All I get is this :
Y =
0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000 0.200000000000000 100 0.200000000000000
i.e the equations are not being solved. I am just getting the initial values of my inputs (i.e x,s,p) as the output.
Any help is appreciated.
1 commentaire
Walter Roberson
le 29 Déc 2013
Should be merged with duplicate http://www.mathworks.co.uk/matlabcentral/answers/110772-solving-3-simultaneous-first-order-differential-equations
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