$
$  Lorenz differential equation :
$
$  x' = sigma*( y - x )
$  y' = rho*x - y - x*z
$  z' = -beta*z + x*y
$
$  sigma,rho,beta > 0
$
$
$ The data after the differential equation (terminated with ;;) means:
$
$ 1 0 20 0 16  :             out = 1,        each 1-st step
$                                            will be printed out
$                        T_start = 0,        start of integration interval
$                        T_end   = 20,       end of integration interval
$                      h_initial = 0,        initial step size chosen by AWA
$                           p    = 16,       order of method
$
$ 4             : enclosure method 4, i.e. intersection of interval-vector
$                 and QR-decomposition
$
$ 0             : output values : 0 = enclosures of the function values
$                                     of the solution
$
$ 15 15 36      : initial values for the solution
$                 x(0) = 15
$                 y(0) = 15
$                 z(0) = 36
$                 these initial values are close to the strange
$                 attractor of the Lorenz equations.
$
$ 1e-16 1e-16   : Error tolerances E_a = 1e-16 and E_r = 1e-16
$
$
$ n             : do not continue integration
$ n             : no further initial values
$ n             : no other differential equation
$


x = U1   y = U2   z = U3

sigma = 10
 beta = 8/3
  rho = 28

F1 = sigma*(y-x)
F2 = (rho-z)*x - y
F3 = x*y - beta*z
;;

1 0 20 0 16

4 0

15 15 36
 
1e-16 1e-16

n
n
n

