Solve a differential equation system with 4th order Runge-Kutta method with three equations

Hi, I'm trying to solve a Lotka-Volterra system with three equations via the 4th order Runge-Kutta method but I'm not being able to solve it.

This is the function I was using to try to solve it.

Any feedback would be helpfull

Thanks!

function [] = runge_kutta_sis(X,Y,Z,x0,y0,z0,a,b,h) %where X Y and Z are my ecuations, x0 y0 and z0 are the initial values. a is initial time and b is final time  
t = a:h:b;
n = length(t);

x=[x0]; y=[y0]; z=[z0];
for i=1:n-1
    j1 = h*A(x(i),y(i),z(i));
    k1 = h*C(x(i),y(i),z(i));
    l1 = h*L(x(i),y(i),z(i));
    
    j2 = h*A(x(i)+j1/2,y(i)+k1/2,z(i)+l1/2,t(i)+h/2);
    k2 = h*C(x(i)+j1/2,y(i)+k1/2,z(i)+l1/2,t(i)+h/2);    
    l2 = h*L(x(i)+j1/2,y(i)+k1/2,z(i)+l1/2,t(i)+h/2);
    
    j3 = h*A(x(i)+j2/2,y(i)+k2/2,z(i)+l2/2,t(i)+h/2);
    k3 = h*C(x(i)+j2/2,y(i)+k2/2,z(i)+l2/2,t(i)+h/2);
    l3 = h*L(x(i)+j2/2,y(i)+k2/2,z(i)+l2/2,t(i)+h/2);
    
    j4 = h*A(x(i)+j3,y(i)+k3,z(i)+l3,t(i)+h);
    k4 = h*C(x(i)+j3,y(i)+k3,z(i)+l3,t(i)+h);
    l4 = h*L(x(i)+j3,y(i)+k3,z(i)+l3,t(i)+h);
    
    x(i+1)= x(i)+(h/6)*(j1+2*j2+2*j3*j4);
    y(i+1) = y(i)+(h/6)*(k1+2*k2+2*k3*k4);
    z(i+1) = z(i)+(h/6)*(l1+2*l2+2*l3*l4);
end
hold on
plot(t, x)
plot(t, y)
plot(t, z)

Answer 1

[James Tursa]

Not sure if you actually use t in your derivative functions, but you are missing that input from your j1, k1, and l1 code:

    j1 = h*A(x(i),y(i),z(i),t(i));  % added t(i)
    k1 = h*C(x(i),y(i),z(i),t(i));  % added t(i)
    l1 = h*L(x(i),y(i),z(i),t(i));  % added t(i)

Note that all of your j, k, l variables already have the h factor applied to them. So this code should not again multiply by h:

    x(i+1) = x(i)+(1/6)*(j1+2*j2+2*j3*j4);  % changed h to 1
    y(i+1) = y(i)+(1/6)*(k1+2*k2+2*k3*k4);  % changed h to 1
    z(i+1) = z(i)+(1/6)*(l1+2*l2+2*l3*l4);  % changed h to 1