Purpose:  1) Verify orders of convergence of the provided palindromic schemes.
=======   2) Show the usage of the provided palindromic schemes.
          3) Show an unconventional schemes for a special kind of ODE:
             y'=f(y), where f(y) is at most quadratic. In fact, OneStep.f
             and allS1.f are written for any system of this kind. But
             f(y) and f'(y) must be provided. For this particular example
             they are provided by fexjex.f.

                                        Ren-Cang Li, June 1, 1996
                                        na.rcli@na-net.ornl.gov

Files in this directory:
=======================

      main.f     ---  Main program 1 for the Lorenz Strange Attractor.
                      It runs with a particular scheme specified 
                      manually at run time and with a fixed stepsize.
                      It outputs y(t) at each time step.
                      (Read main.f for detail.)

      mainHs.f   ---  Main program 2 for the Lorenz Strange Attractor.
                      It runs with a particular scheme specified 
                      manually at run time and with several different
                      stepsizes, each of which is half of the previous
                      run. It outputs errors for each component of computed
                      y(t) at t=1 for each different stepsize. The output
                      can be used to verified orders of convergence
                      of palindromic schemes.
                      (Read mainHs.f for detail.)
                      
     Makefile    ---  Make file.

     OneStep.f   ---  Provide a reflexive update formula for the above
                      mentioned systems.

     allS1.f     ---  Call OneStep.f repeatedly to yield any particular
                      palindromic scheme.

     The following routines are from LAPACK and BLAS:
     --- --------- -------- --- ---- ------ --- ----

       dgemm.f dger.f  dgesv.f dgetf2.f dgetrf.f dgetrs.f dlaswp.f
       dscal.f dswap.f dtrsm.f fexjex.f idamax.f ilaenv.f lsame.f 
       xerbla.f

Files in subdrectory ErrAtT=1:
===== == =========== ========

    Results1 to Results15 are the outputs of mainHs.f for
    15 palindromic schemes, running on a IBM RS6000/590.
