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+## Copyright (C) 2011 Carlo de Falco
+## 
+## 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 Octave; see the file COPYING.  If not, see
+## <http://www.gnu.org/licenses/>.
+
+## Author: Carlo de Falco <carlo@guglielmo.local>
+## Created: 2011-12-24
+
+
+%% you need at least version 3.4 of Octave to run this script
+
+clear all
+close all
+
+%% uncomment the following line if you don't have the required packages installed
+%% pkg install -forge general bim fpl msh splines
+pkg load general bim fpl msh splines
+
+%%%%%%%%%%%%%%%%%%%%%
+%%%    SERIAL VERSION
+%%%%%%%%%%%%%%%%%%%%%
+
+tic ();
+nel = 100;
+U0 = randn (200, 1);
+us = zeros (101, 200);
+for ii=1:numel (U0)
+
+  x = transpose (linspace (0, 1, nel+1));
+  A = bim1a_laplacian (x, 1, 1);
+  b = bim1a_rhs (x, 1, 1);
+
+  us(:,ii) = zeros (size (x));
+  us(1,ii) = U0(ii);
+  
+  res = @(X) A(2:end-1, 2:end-1) * X - (b(2:end-1) - A(2:end-1, [1 end]) * us([1 end], ii));
+  us(2:end-1,ii) = fsolve (res, us(2:end-1,ii));
+
+endfor
+toc ()
+
+
+
+
+%%%%%%%%%%%%%%%%%%%%%
+%%%  PARALLEL VERSION
+%%%%%%%%%%%%%%%%%%%%%
+
+%% solve  - u'' + exp (u) = 1 in (0, 1) with u(0)=u0 and u(1)=0
+function u = poisson1d (u0)
+  nel = 100;
+  x = transpose (linspace (0, 1, nel+1));
+  A = bim1a_laplacian (x, 1, 1);
+  b = bim1a_rhs (x, 1, 1);
+
+  u = zeros (size (x));
+  u(1) = u0;
+  
+  res = @(X) A(2:end-1, 2:end-1) * X - (b(2:end-1) - A(2:end-1, [1 end]) * u([1 end]));
+  u(2:end-1) = fsolve (res, u(2:end-1));
+endfunction
+tic ();
+U0 = num2cell (randn (1, 200));
+up = parcellfun (2, @poisson1d, U0, "UniformOutput", true, "VerboseLevel", 2);
+toc ()
+
+%subplot (1, 2, 1)
+%plot (x, us)
+%subplot (1, 2, 2)
+%plot (x, up)
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