This folder contains one folder, four Matlab files and this readme file.

The 'report' folder contains LaTeX source, figures, and output. 
The file fem_neuman.pdf is an Adobe PDF file of the report and describes the construction of a finite element model for a (class of) reaction diffusion problems with zero Neuman boundary data.

The Matlab files implement the ideas in the report.

1)
rd_fem.m is a script file that specifies problem data, then invokes solver and plot procedures. Problem data (in rd_fem,m) are as follows:
  w_0    = @(x) sin(pi*x); % initial temperature
 
  c_array= [0; -1; 0; 1];  % coefficients of nonlinear reaction term
  
  
  t_array= (0:.04:4);      % time array for output
  
  n      = 32;             % grid parameter

2)
rd_lin_spline.m organizes the main calculations. It assembles mass and stiffness matrices, the vector of initial conditions and assigns a 'handle' to the right-hand-side function of our approximating ODE system. Internal functions organize the evaluation of the nonlinear reaction term (a 3rd order polynomial).

3)
plot_rd.m generates a surface plot of the space time evolution as well as a time history of the squared-norm of the solution.

4)
basic_hat.m defines a 'basic' hat function on the interval [-1, 1]. The spline bases functions are 'shifted' versions of this function. It appears at this level so that it is available  for use in defining an initial condition.