function errors_test15 ( )

%*****************************************************************************80
%
%% ERRORS_TEST15
%
%  Licensing:
%
%    This code is distributed under the GNU LGPL license.
%
%  Modified:
%
%    22 August 2017
%
%  Author:
%
%    John Burkardt
%
  fprintf ( 1, '\n' );
  fprintf ( 1, '+=============================================+\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  Exercise 15                                |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    F(X) =       ( 4970 * X - 4923 )         |\n' );
  fprintf ( 1, '|           --------------------------------  |\n' );
  fprintf ( 1, '|           ( 4970 * X^2 - 9799 * X + 4830 )  |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  Approximate F"(X) at X = 1 by:             |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    Del2(X)(F,H) =                           |\n' );
  fprintf ( 1, '|      ( F(X-H) - 2*F(X) + F(X+H) ) / H^2     |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|  Correct values:                            |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    F"(1.0)             = 94.0               |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '|    Del2(1.0)(F,1.0E-4) = 70.78819           |\n' );
  fprintf ( 1, '|    Del2(1.0)(F,1.0E-5) = 93.76790           |\n' );
  fprintf ( 1, '|    Del2(1.0)(F,1.0E-8) = 94.0               |\n' );
  fprintf ( 1, '|                                             |\n' );
  fprintf ( 1, '+=============================================+\n' );
  fprintf ( 1, '\n' );
  fprintf ( 1, '  H                Del2(X,H)\n' );

  x = 1.0;

  for i = 1 : 3

    if ( i == 1 )
      h = 1.0E-04;
    elseif ( i == 2 )
      h = 1.0E-05;
    elseif ( i == 3 )
      h = 1.0E-08;
    end

    r = ( fx15 ( x + h ) - 2.0 * fx15 ( x ) + fx15 ( x - h ) ) / h ^ 2;

    fprintf ( 1, '  %20.16g  %20.16g\n', h, r );

  end

  return
end

