Help with Runge-Kutta Order 4th with a system of 3 equations

61 Views Asked by At

I have been trying to solve a system of equations with Runge-Kutta Order 4th but every time I try to run the program it says running but it doesn't load anything so I can't check if it is good or not. Can anyone tell me if it's ok or what should I change about it? The code is written in Wolfram Mathematica. This is the problem I replaced rho sigma and beta with v, i and c

Clear[f, g, u, k1, k2, k3, k4, v, i, j, c, l1, l2, l3, l4, p1, p2, p3, p4]
v = 28
i = 10
c = 15

j = 3
Subscript[x, 0] = 1
Subscript[y, 0] = 1
Subscript[z, 0] = 1
Subscript[t, 0] = 0
a = 0
b = 1
h = (a + b)/j 
f[Subscript[x, n] _, Subscript[y, n] _, Subscript[z, n] _, 
  Subscript[t, n] _] := v*(Subscript[y, n] - Subscript[x, n])
g[Subscript[x, n] _, Subscript[y, n] _, Subscript[z, n_], 
  Subscript[t, n] _] := 
 Subscript[x, n]*(i - Subscript[z, n]) - Subscript[y, n]
u[Subscript[x, n_], Subscript[y, n] _, Subscript[z, n] _, 
  Subscript[t, n] _] := 
 Subscript[x, n]*Subscript[y, n] - c*Subscript[z, n]
For[
 n = 0, n < j, n++; Subscript[t, n] = Subscript[t, 0] + h,
 k1 = f[Subscript[x, n], Subscript[y, n], Subscript[z, n], Subscript[
   t, n]];
 l1 = g[Subscript[x, n], Subscript[y, n], Subscript[z, n], Subscript[
   t, n]];
 p1 = u[Subscript[x, n], Subscript[y, n], Subscript[z, n], Subscript[
   t, n]];
 k2 = f[Subscript[x, n] + h/2*k1, Subscript[y, n] + h/2*l1, 
   Subscript[z, n] + h/2 + p1, Subscript[t, n] + h/2];
 l2 = g[Subscript[x, n] + h/2*k1, Subscript[y, n] + h/2*l1, 
   Subscript[z, n] + h/2 + p1, Subscript[t, n] + h/2];
 p2 = u[Subscript[x, n] + h/2*k1, Subscript[y, n] + h/2*l1, 
   Subscript[z, n] + h/2 + p1, Subscript[t, n] + h/2];
 k3 = f[Subscript[x, n] + h/2*k2, Subscript[y, n] + h/2*l2, 
   Subscript[z, n] + h/2 + p2, Subscript[t, n] + h/2];
 l3 = g[Subscript[x, n] + h/2*k2, Subscript[y, n] + h/2*l2, 
   Subscript[z, n] + h/2 + p2, Subscript[t, n] + h/2];
 p3 = u[Subscript[x, n] + h/2*k2, Subscript[y, n] + h/2*l2, 
   Subscript[z, n] + h/2 + p2, Subscript[t, n] + h/2];
 k4 = f[Subscript[x, n] + h*k3, Subscript[y, n] + h*l3, 
   Subscript[z, n] + h*p3, Subscript[t, n] + h];
 l4 = g[Subscript[x, n] + h*k3, Subscript[y, n] + h*l3, 
   Subscript[z, n] + h*p3, Subscript[t, n] + h];
 p4 = u[Subscript[x, n] + h*k3, Subscript[y, n] + h*l3, 
   Subscript[z, n] + h*p3, Subscript[t, n] + h];
 Subscript[x, n + 1] = Subscript[x, n] + (h/6)*(k1 + 2*k2 + 2*k3 + k4);
 Subscript[y, n + 1] = Subscript[y, n] + (h/6)*(l1 + 2*l2 + 2*l3 + l4);
 Subscript[z, n + 1] = Subscript[z, n] + (h/6)*(p1 + 2*p2 + 2*p3 + p4);
 ]

I will also add an image with the code just in case The code written in Mathematica