2 views (last 30 days)

Hello,

suppose I've got four equations which depend on one another and one of them depends on the time:

a = f(b);

b = f(c);

c = f(d);

d = f(a,t);

How can a system like this be solved? I thought about using one of the ode solvers but failed to implement the functions. Can anybody give me a hint?

Thanks in advance,

J

Isktaine
on 14 Aug 2012

Edited: Isktaine
on 14 Aug 2012

You need to have a function which the ode solvers can act on.

[t,y] = ode45('YourODEFunction', [0 50], [a(0) b(0) c(0) d(0)])

An example of how to create the function:

function dA=YourODEFunction(x,A)

dA(1)=f(b); %Equation for a,

dA(2)=f(c); %Equation for b

dA(3)=f(d); %Equation for c

dA(4)=f(a,t); %Equation for d

dA=dA'

Note that when you have f(b) (and all the others) you'd have to type in an experission eg

dA(1)=3*A(2) %Coding up of a=3*b

Any time your equation would have a 'b' use A(2), any time you would use an 'a' use A(1), any time you would use a 'c' use A(3) and 'd' use A(4). Does that make sense?

Isktaine
on 17 Aug 2012

I'm sorry! I think I misunderstood your first question then. I was assuming all of these were differentials i.e. a'=f(b). How silly of me to make that assumption! Are any of the equations actually differentials?

If there are no differentials then you have to uncouple the system before it can solved numerically. You could just use direct substitution to solve them by hand to get one equation for d only in terms of t, the use back substitution to find values for c,b and a once you have d for any t.

Find the treasures in MATLAB Central and discover how the community can help you!

Start Hunting!
## 1 Comment

## Direct link to this comment

https://la.mathworks.com/matlabcentral/answers/45975-how-do-i-solve-a-system-of-equations#comment_94648

⋮## Direct link to this comment

https://la.mathworks.com/matlabcentral/answers/45975-how-do-i-solve-a-system-of-equations#comment_94648

Sign in to comment.