Solving 3 simultaneous first order differential equations

Question

Abhivyakti 2013-12-29

0
链接

此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110952-solving-3-simultaneous-first-order-differential-equations

评论： Walter Roberson 2013-12-29

采纳的回答： Azzi Abdelmalek

在 MATLAB Online 中打开

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.

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Walter Roberson 2013-12-29

Should be merged with duplicate http://www.mathworks.co.uk/matlabcentral/answers/110772-solving-3-simultaneous-first-order-differential-equations

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Answer 1

Azzi Abdelmalek 2013-12-29

0
链接

此回答的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/110952-solving-3-simultaneous-first-order-differential-equations#answer_119590

在 MATLAB Online 中打开

Because in react function you added

y=zeros(3,1);

Remove this line

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Abhivyakti 2013-12-29

Thankyou soo much! That worked.

Another doubt I have. I need to plot the graphs of 'dx/dt vs t', 'ds/dt vs t' and 'dp/dt vs t'.

I cannot figure out how to get an equation between 'dx/dt and t' , i.e how to consider the variation of 'dx/dt' with 't' in one equation as 'dx/dt varies as the variation of 's' & 'p' wrt 't'.

Abhivyakti 2013-12-29

Basically , I think if I have the equation of each 'x' with respect to 't', I can differentiate that & obtain 'dx/dt'. So, can I get the equation of 'x' wrt 't' ( as its obtained using function dsolve) by using 'ode23 or ode45' ????

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