Example 4.  Solve the Lorenz I. V. P.
          
          
          
Use Mathematica's NDSolve procedure.  

Solution 4.

Caution. The syntax must be followed carefully.  The symbol " is the boolean equal, you can use two ordinary equal signs next to each other if you prefer ".  

Mathematica's numerical D.E. solver.  It is more robust than the Runge-Kutta method, we can solve the D.E.'s over the larger interval  .  

Caution.  If you do not use the option  "" then Mathematica will give you the error message:

NDSolve::"mxst": "Maximum number of 1000 steps reached at the point t == 11.146875180780313`."

After you solve the problem successfully, you should make copies of the commands and delete the MaxSteps option so you can see "numerical analysis in action."  (Or the lack of it, because no one wants to report a bad answer.)

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(c) John H. Mathews 2004