# How to solve fick's 2nd law of diffusion equation?

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Nonlinear on 21 Nov 2017
Commented: Nonlinear on 24 Nov 2017
Hello everybody,
I am trying to solve a PDE which has the form:
dC/dt = (1+c)^2/{(1+c)^2+1}d2C/dx2
Can Matlab solve such a equation like that? If it can, how can I set it up?
Thanks for any help.

Precise Simulation on 22 Nov 2017
Modeling and simulation of convection and diffusion is certainly possible to solve in Matlab with the FEA Toolbox, as shown in the model example below:
% Set up 1D domain from 0..1 with 20 elements.
fea.sdim = { 'x' };
fea.grid = linegrid( 20, 0, 1);
% Add covection and diffusion physics mode.
fea = addphys( fea, @convectiondiffusion, {'C'} );
% Define diffusion coefficient.
fea.phys.cd.eqn.coef{2,end} = {'d_coef'};
fea.expr = { 'c', {'1.23'} ;
'd_coef', {'(1+c)^2/((1+c)^2+1)'} };
% Use c = -1 on right boundary, and insulation
% flux boundary conditions on the left.
fea.phys.cd.bdr.sel = [ 1 3 ];
fea.phys.cd.bdr.coef{1,end}{1} = -1;
% Check, parse, and solve problem
% with initial condition 'C=2*x'.
fea = parsephys( fea );
fea = parseprob( fea );
[fea.sol.u,tlist] = ...
solvetime( fea, 'dt', 0.1, 'tmax', 1, 'init', {'2*x'} );
% Alternatively, solvestat can be used for stationary problems.
% Postprocessing.
isol = length(tlist);
postplot( fea, 'surfexpr', 'C', 'solnum', isol )
title( ['Solution at time, t = ',num2str(tlist(isol))] )
ylabel( 'Concentration, C' )
Nonlinear on 24 Nov 2017
Thank you very much for your help.