  ***************************************************************************
  * All the software  contained in this library  is protected by copyright. *
  * Permission  to use, copy, modify, and  distribute this software for any *
  * purpose without fee is hereby granted, provided that this entire notice *
  * is included  in all copies  of any software which is or includes a copy *
  * or modification  of this software  and in all copies  of the supporting *
  * documentation for such software.                                        *
  ***************************************************************************
  * THIS SOFTWARE IS BEING PROVIDED "AS IS", WITHOUT ANY EXPRESS OR IMPLIED *
  * WARRANTY. IN NO EVENT, NEITHER  THE AUTHORS, NOR THE PUBLISHER, NOR ANY *
  * MEMBER  OF THE EDITORIAL BOARD OF  THE JOURNAL  "NUMERICAL ALGORITHMS", *
  * NOR ITS EDITOR-IN-CHIEF, BE  LIABLE FOR ANY ERROR  IN THE SOFTWARE, ANY *
  * MISUSE  OF IT  OR ANY DAMAGE ARISING OUT OF ITS USE. THE ENTIRE RISK OF *
  * USING THE SOFTWARE LIES WITH THE PARTY DOING SO.                        *
  ***************************************************************************
  * ANY USE  OF THE SOFTWARE  CONSTITUTES  ACCEPTANCE  OF THE TERMS  OF THE *
  * ABOVE STATEMENT.                                                        *
  ***************************************************************************

   AUTHOR:

       Slawomir Milewski
       Civil Engineering Department
       Cracow University of Technology, Cracow, Poland
       slawek@L5.pk.edu.pl

       
   REFERENCE:

    -  Selected computational aspects of the meshless finite 
       difference method
       NUMERICAL ALGORITHMS, 63 (2013), pp. 107-126

   SOFTWARE REVISION DATE:

       V1.0, June 2012

   SOFTWARE LANGUAGE:

       Matlab 7.7

=====================================================================
PACKAGE
=====================================================================

The directory contains the following files

README             	:  this file
Contents.m		:  general help page, which is displayed in Matlab
star.m 			:  source code of the MFD star generation procedure, 
			   based on the distance criterion
localMFDM.m 	        :  source code of the MFDM solution approach 
			   for problem posed in local formulation
varMFDM.m 	   	:  source code of the MFDM solution approach 
			   for problem posed in variational (Galerkin) 
			   formulation
postprocessingMFDM.m	:  source code for the postprocessing based on 
			   the MFDM results and MWLS approximation technique
railroadrailDATA.txt    :  required data for the MFDM analysis of the railroad 
			   rail
mwls.m			:  the function file which contains the MWLS procedure 
			   in order to obtain the difference formulas for 
			   subsequent derivatives on the basis of the  m  star 
			   nodes, approximation order (p) and 
			   smoothing parameter (g).
TEST.m			:  the script file which runs all m-files, in which the 
			   discretization of the domain is prepared, dependently 
			   on the task type (task variable) and problem 
			   formulation (formulation variable).

==========
COMPILER
==========

The Matlab code has to be run through the Matlab environment directly and, 
therefore it does not require any compilation.

=====================================================================
HOW TO INSTALL
=====================================================================

The user is supplied with one zip file which contains one directory with 
all necessary files in it. This archive file should be uncompressed to 
the prescribed location. 

==========
LIBRARIES
==========

This program package does not require any external libraries. 
It uses Matlab built-in functions as well as some functions from 
the standard Matlab toolboxes.

================
RUN THE PROGRAMS
================

The only m-file from this directory, which may be run directly, 
is the TEST.m file. One may add the name of this directory to the Matlab 
search path in order to run this file from the Matlab Command Line from any 
other directory. In other cases, the user should open the file with an
editor and run it, after changing the Matlab working directory. 
Note that for any changes in the data structure, it is required to open 
this file with an editor.

=====================
RUN TEST
=====================

To test the software, run the TEST.m program without any changes 
within its structure. One should observe:

Command Window: text results (nodal and element values) should be displayed.
Right values are given inside the manual.

Maltab figure: four graphs, containing the graphical 3D view of the nodal 
results.

To perform any changes in data structure, edit TEST.m and change default 
values of variables (teta,G,task,formulation,a,b,nx,ny). 
Afterwards, save changes and run the program.

