three_midpoint.m

## Copyright (C) 2016 Wesley
## 
## This program is free software; you can redistribute it and/or modify it
## under the terms of the GNU General Public License as published by
## the Free Software Foundation; either version 3 of the License, or
## (at your option) any later version.
## 
## This program is distributed in the hope that it will be useful,
## but WITHOUT ANY WARRANTY; without even the implied warranty of
## MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
## GNU General Public License for more details.
## You should have received a copy of the GNU General Public License
## along with this program.  If not, see <http://www.gnu.org/licenses/>.

## -*- texinfo -*- 
## @deftypefn {Function File} {@var{retval} =} three_midpoint (@var{input1}, @var{input2})
##
## @seealso{}
## @end deftypefn

## Author: Wesley <Wesley@WESLEYPC>
## Created: 2016-05-17

function [retval] = three_midpoint (f, x0, x2, h)
% approximate the third derivative error term in problem 1 to be 6
% proof given in hand-written part
retval = 1/(2*h)*(f(x2)-f(x0))-h^2/6*6
endfunction