Non-linear differential dquation

Hi everyone,

I am trying to solve the non-linear differential equation which has form:

What I'm thinking is using pdepe, but as the equation is quite complicated to me, I really don't know how to solve it.

Could anyone please help me solving this problem?

I would appreciate any kind of you help.

Thank you.

Answer 1

[Precise Simulation]

As per your previous question https://www.mathworks.com/matlabcentral/answers/368440-how-to-solve-fick-s-2nd-law-of-diffusion-equation

    % Set up 1D domain from 0..3 with 20 elements.
    fea.sdim = { 'x' };
    fea.grid = linegrid( 20, 0, 3 );

    % Add covection and diffusion physics mode.
    fea = addphys( fea, @convectiondiffusion, {'u'} );

    % Define diffusion coefficient.
    fea.phys.cd.eqn.coef{2,end} = {'d_coef'};
    fea.expr = { 'd_coef', {'0.00296*(1+49*u)^2/((1+49*u)^2+0.00164)'} };

    % Use u = 0 on left boundary (x=0), and insulation
    % flux boundary du/dx=0 conditions on the right (x=3).
    fea.phys.cd.bdr.sel = [ 1 3 ];
    fea.phys.cd.bdr.coef{1,end}{1} = 0;

    % Check, parse, and solve problem 
    % with initial condition 'u=0.01'.
    fea = parsephys( fea );
    fea = parseprob( fea );

    [fea.sol.u,tlist] = ...
        solvetime( fea, 'tstep', 10, 'tmax', 100, 'init', {'0.01'} );
    % Alternatively, solvestat can be used for stationary problems.

    % Postprocessing.
    isol = length(tlist);
    postplot( fea, 'surfexpr', 'u', 'solnum', 1 )
    hold on
    postplot( fea, 'surfexpr', 'u', 'solnum', floor(isol/2) )
    postplot( fea, 'surfexpr', 'u', 'solnum', isol )
    axis normal
    grid on
    title( ['Solution at times, t = ',num2str(tlist([1 floor(isol/2) isol]))] )
    ylabel( 'Concentration, u' )

[Nonlinear]

Again, thank you for your kind explanation. Is this FEA tool box can be operated in mac os?