How do I solve a system of equations?

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Julian Laackmann 2012-8-14

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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,

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Walter Roberson 2012-8-15

I am confused about you using f() with one argument in most places, but using it with two arguments for "d".

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Isktaine 2012-8-14

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编辑：Isktaine 2012-8-14

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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?

You may find this useful: http://www.math.vanderbilt.edu/~daphne/courses/math226/MatlabODEs.pdf

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.

Julian Laackmann 2012-9-11