Hello,
I need help with a home asignment I have for a matlab course. The aim is to solve P and Z for the two functions dP/dt and dZ/dt. I have managed to write the code in ah_alg.m, the function in lorenz and the rk4 in rk4 files. However, I get the wrong answer and as such, my error function is wrong.
The asignment is to a) solve for P and Z. b) Plot the error function for P and Z by calculating |P(n)h/2 - P(n)h| where P(n)h is P with regular steplength, P(n)h/2 is steplength halved.
dP/dt = rP (1 - P2/α2 + P2) - RmZ
dZ/dt = γRmZ P/(K + P) - μZ
This is a breif summary of the asignment, the whole thing can otherwise be found in proj1mat_eng.pdf. As mentioned, my code runs, but produces the wrong result. Can anyone look through my code files and see whats wrong or is it better to start over?
pout = rk4(@(t,x)lorenz(t,x,K,R,r,alpha,mu,gamma),h,time,xin);
pout2 = rk4(@(t,x)lorenz(t,x,K,R,r,alpha,mu,gamma),h2,time,xin2);
Err(1,i) = abs(pout2(1)-pout(1));
Err(2,i) = abs(pout2(2)-pout(1));
plot(log(tspan(1,:)),log(Err(1,:)))
plot(log(tspan(1,:)),log(Err(2,:)))
function dp = lorenz(t,x,K,R,r,alpha,mu,gamma)
r*x(1)*(1-x(1)/K) - R*x(2)*(x(1)^2/(alpha^2 + x(1)^2));
gamma*R*x(2)*(x(1)/(alpha^2 + x(1)^2)) - mu*x(2);
function pout = rk4(f,h,tk,xk)
k2 = f(tk+h/2,xk+h*k1/2);
k3 = f(tk+h/2,xk+h*k2/2);
pout = tk + (h/6)*(k1+k2+k3+k4);
