Simple system of ODES with starting condition

opts = odeset('RelTol',1e-15,'AbsTol',1e-20);

X0 = [ 0.9 0.1 0 ];

[T X] = ode45(@(t,X)returnDerivative(t, X), [0 10], X0,opts) ;

plot(T,X);

function dXdt = returnDerivative(t, y)

dXdt = [-1/2*y(1)*y(3) ; 1/3*y(3) ; 1/2*y(1)*y(3) - 1/3*y(3)];

end

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I am trying to solve this simple system of ODEs but it returns me constant solutions for X(1),X(2) and X(3)

and dimension of X is only 41 x 3 .Can someone explain me where is my mistake?

And what is in general best way to solve this kind of system of ODEs

[Rik]

Even if you think it is a stupid question and you found the mistake, it is still rude to edit away your question. Someone else might stumble on your question and the answer and learn something from it. Leaving your question as it was is the least you can do.

[Velimir Corovic]

if I thought thst someone could learn from my question I wouldn't remove it , the question wasn't good because my concetration was very bad and I miscoded initial condtions.That's the reason of deleting question.

[Star Strider]

If you want to re-post the corrected question, please do so.

[Rena Berman]

(Answers Dev) Restored edit

Answer 1

[Star Strider]

The only (relative) mistake I can see is that it is not good to use global variables. Pass the values as extra parameters instead.

This works:

b=1/2;
k=1/3;
opts = odeset('RelTol',1e-15,'AbsTol',1e-20);
X0 = [ 1 0.00001  0 ];
[T X] = ode45(@(t,X)returnDerivative(t, X, b, k), [0 10], X0,opts) ;

plot(T,X);
function dXdt = returnDerivative(t, y, b, k) %X je vektor 4Nx1
        dXdt = [-1/2*y(1)*y(3) ; 1/3*y(3) ; 1/2*y(1)*y(3) - 1/3*y(3)];
end

What result were you expecting?

[Star Strider]

I cannot find anything wrong with your code.

If you are copying a system of ODEs and may haave mis-coded them, please post the original (symbolic) expressions and initial conditions. I will see if I can find the error.