Runge-Kutta 3 variables, 3 equations

I am trying to use the 4th order Runge Kutta method to solve the Lorenz equations over a perios 0<=t<=250 seconds. I am able to solve when there are two equations involved but I do not know what do to for the third one. I have :

x(1)=1;
y(1)=2;
z(1)=0;

h=0.1;

sigma=10;
rho=28;
beta=(8/3);

f=sigma*(y-x);
g=rho*x-y-x*z;
w=x*y-beta*z;

for i=1:2500
    k1=h*f(x(i),y(i),z(i));
    l1=h*g(x(i),y(i),z(i));
    m1=h*w(x(i),y(i),z(i));

I do not know what to do when calculating k2 etc. I have:

k2=f(x(i)+h/2, y(i)+k1/2, z(i)+l1/2);

etc. but is there any change with m(i)? I only know how to solve this for two equations. Am I on the right track? I'm new to MATLAB and Runge-Kutta so any help would be greatly appreciated.

[Miguel Buitrago]

I used the 4th order Runge Kutta method to solve the Lorenz equations:

   k1 = h*f(u1,u2);
   m1 = h*g(u1,u2,u3);
   n1 = h*e(u1,u2,u3);
   k2 = h*f(u1+k1/2, u2+m1/2);  
   m2 = h*g(u1+k1/2, u2+m1/2, u3+n1/2);  
   n2 = h*e(u1+k1/2, u2+m1/2, u3+n1/2);  
   k3 = h*f(u1+k2/2, u2+m2/2);
   m3 = h*g(u1+k2/2, u2+m2/2, u3+n2/2);  
   n3 = h*e(u1+k2/2, u2+m2/2, u3+n2/2);
   k4 = h*f(u1+k3, u2+m3);
   m4 = h*g(u1+k3, u2+m3, u3+n3);
   n4 = h*e(u1+k3, u2+m3, u3+n3);

   u1 = u1 + (k1+(k2*2)+(k3*2)+k4)/6;
   u2 = u2 + (m1+(m2*2)+(m3*2)+m4)/6;
   u3 = u3 + (n1+(n2*2)+(n3*2)+n4)/6;

[SHIVANI TIWARI]

Runge-kutta third order method:

%rk3:runge kutta of thirdorder

clc;

clear all;

close all;

% y' = y-x ode condition

f = @(x,y) y-x;

fex = @(x) exp(x)+x+1; % exact solution

a=0;

b= 3.2;

n =16;

h=(b-a)/n;

y(1) =2; %initial value

i = 0;

for x= a:h:b

i = i+1;

K1 = f(x,y(i)); %initializing solution

K2 = f(x+h*0.5,y(i)+h*K1*0.5);

K3 = f(x+h, y(i)-h*K1 +2*K2*h);

y(i+1) =y(i)+h*(1/6)*(K1 +4*K2+K3);

g(i) = fex(x);

xx(i) = x;

Error(i) = abs(g(i) - y(i)); %error obtain

end

%plot result

plot(xx,y(1:n+1),'k',xx,g,'y')

legend('RK3','Exact solution')

xlabel('x')

ylabel('y')

title('RK3 vs exact solution')

can you plz check my code.actually i dont get exact error. so plz check my prgram