使用ode45函数时odefun的输入变量是什么？

Question

I am trying to solve a quite simple ODE (1. order reaction rates) with the function ode45, but while I am able to do that successfully, I am not 100% sure what is actually happening. This is the code for reference:

x0 = [0.1,0.1];
tspan = [0, 10];
k = [1, 1];

[t_a, x_a] = ode45(@odefun, tspan, x0, [], k);


plot(t_a, x_a)
xlabel('t')
ylabel('x')
legend('A','B')

function dxdt = odefun(t,x,k)
    k1  = k(1);
    dxdt = zeros(2,1);
    dxdt(1) = -2*k1*x(1)*x(1);
    dxdt(2) = k1*x(1)*x(1);
end

This yields the expected results, but what I do not understand is, what the input parameter of odefun actually are (I know what they represent, but not how they were created, as I never defined them). The documentation was no great help for that, so I am wondering, where are the coming from? Are they provided by ode45? If so how is that possible when odefun is an input of ode45?

Obviously this code is not fully written by me, so, to be more specific, I have trouble understanding how I know I have to use x(1).

Thanks for your help!

Answer 1

The t and x inputs are generated by ode45 based on the initial values of t and x which you provide. ode45 calls the function with new values of t and x as it solves the problem, with the new values being based on the output of your function.