ODE45 how do I interpret this code...

if true
  % code
end
function elements 
tspan = [0 1];
inits = [0 1];
[t,y] = ode45(@Y,tspan,inits);
plot(t,y)
function deriv = Y(t,y)
deriv = zeros(size(y));
deriv(1) = y(2) ;
deriv(2) = -y(1);
% the same as deriv = [y(2); -y(1)]

The first part I understand y is created and initiate with a vector [ 0 1 ] which is the initial condition. However the part deriv(1) = y(2) and the following line confuses me. I think that since y was created when matlab goes to the function deriv it will see the function as deriv(1) = 1 and deriv(2) = -0 since y exists... However the code works and matlab sees the function ( I mean the Y's ) as variables y1 and y2 ... Could anyone clarify this to me please. How does MATLAB read this... Sorry that's my second question about it. I don't think I got it.. I've already read doc ode45 and doc function it's not clear in there.

Answer 1

[Sara]

When you call an ode solver, the values of y passed to your function Y change in time and depend on numerical method, in this case a Runge-Kutta.

The mathematical meaning of the code is that, given 2 variables y1 and y2, then their derivatives in time can be written as:

dy1/dt = y2

dy2/dt = -y1

What system this is I have no idea.

What is your problem with this code??

[Douglas Alves]

The code is ok. But I don't get the syntax. Because y is defined by the initial values. And it happens before I enter ode45 so when the function Y is called there must be an erro because instead of y(2) be a variable it could be the second element of y .. Why not? See my confusion?

[Sara]

"because instead of y(2) be a variable it could be the second element of y" ... I don't get what you mean with this.

You don't go directly from your code to the Y function. You pass the initial conditions to ode45 and a time range, then ode45 calls Y as many times as needed with different values of y (where y is an array of 2 elements, corresponding to 2 different variables). Do you have know what a Runge-Kutta is? What the ode45 does is calculating the evolution in time of y(1) and y(2).