Initial condition of y(0) = 1

I am solving a differential equation (dy/dt = (-1/2*y*sin^2(t)) where y(0)=1) using different methods for my homework. For the Runge-Kutta method I keep getting the error: "Subscript indices must either be real positive integers or logicals."

I know that the y(0) = 1 initial condition is the problem, and that there just can't be a 0 in the parentheses, but I have know idea how to correct this? How can I put in the initial condition and make the program run. Below is the code that I am using if you need it.

clear;
clc;
h = input('What would you like the time step to be? >> ');
x = 0:h:10*pi;
y = zeros(1,length(x));
y(0) = 1;
F_xy = @(t,y) ((-1/2)*y*(sin(t)*sin(t)));
for i = 1:(length(x)-1)
  k_1 = F_xy(x(i),y(i));
  k_2 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_1));
  k_3 = F_xy((x(i)+0.5*h),(y(i)+0.5*h*k_2));
  k_4 = F_xy((x(i)+h),(y(i)+k_3*h));

    y(i+1) = y(i)+(1/6)*(k_1+2*k_2+2*k_3+k_4)*h;
end

Answer 1

[Torsten]

Just put it

y(1) = 1.0;

The '0' does not refer to the spatial x-value, but is an array index. Keep in mind that x(1)=0, and y(1) is the solution value at x(1).

Best wishes

Torsten.