MATLAB: Heun mthod 1st order ode

heun

Is this code correct and how do i find which integer time t is the solution y(t) closest to -0.2
y0 = -1;                  % Initial Condition
h = 0.1;
t = 0:h:100;              
y_heun = zeros(size(t));  % Preallocate array (good coding practice)
% Initial condition gives solution at t=0.
y_heun(1) = y0;
% Solving the equation via Heun's method
for i=1:(length(t)-1)
    k2 = sqrt(t(i)+(y_heun(i)^2))-sqrt(t(i)) % Previous approx for y gives approx for derivative
    y_heun(i+1) = y_heun(i) +  h*k2;
    k3 = sqrt(t(i+1)+(y_heun(i+1)^2))-sqrt(t(i+1)));  
    y_heun(i+1) = y_heun(i) + (h/2)*(k3+k2); % Approximate solution for next value of y
end

Best Answer

"Using intervals of delta t=1" does not mean 
h = 0.1;
t = 0:h:100;
but h=1. Then the 2nd question is easy:
[value, index] = min(abs(y_heun - (-0.2)))
Remember, that the time starts at 0, but the index at 1.
Related Question