**LORENTZ EQUATIONS**

**dx/dt = S*(y-x)**

**dy/dt = R*x
- y - x*z**

**dz/dt = x*y -B*z**

Is a system of 3 coupled, non-linear differential equations for the three variables x(convective flow), y(horizontal temperature), z(vertical temperature).

USE:

**S (Prandtl Number) = 10,**

**R (Rayleigh Number) = 28,**

**B (vertical to horizontal size ratio) = 8/3,**

**Initial values: x0 = z0 = 0, y0 =1**

**Note: The equations cannot be "solved" analytically,only
numerically (using, for instance, Euler's method, with D="delta"):**

**dx/dt = "xdot"= lim (Dt-->0) {Dx/Dt}=**

**=approx. Dx/Dt
---->**

**x(t +Dt) =approx.
x(t) + xdot*Dt**