# Error in solving system of two reaction-diffusion equations?

Hello there,

I have a system of two reaction-diffusion equations that I want to solve numerically (attached is the file). However, it doesn't resemble with the standard system used in pdepe.m example. The problems I have are:

**(1)** I don't know how to incorporate it and write c, f, s for my system. As per my knowledge the problem is with the extra term $\gamma \partial u/\partial x$.

**(2)** I tried coding it up but I got an error:

**Warning: Failure at t=2.806210e-02. Unable to meet integration tolerances without reducing the step size below
the smallest value allowed (5.551115e-17) at time t.
> In ode15s (line 730)
In pdepe (line 289)
In pde_bee (line 67)**

Here is the code I wrote:

m = 0; % not sure what m should be for my system of equations x = [0 0.005 0.01 0.05 0.1 0.2 0.5 0.7 0.9 0.95 0.99 0.995 1]; t = [0 0.005 0.01 0.05 0.1 0.5 1 1.5 2];

sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t); u1 = sol(:,:,1); u2 = sol(:,:,2);

figure; surf(x,t,u1); title('u1(x,t)'); xlabel('Distance x'); ylabel('Time t');

figure; surf(x,t,u2); title('u2(x,t)'); xlabel('Distance x'); ylabel('Time t');

% --------------------------------------------------------------------------

function [c,f,s] = pdex4pde(x,t,u,DuDx) delta = 0.5; gamma = 0.1; alpha = 0.1; beta = 0.1; muB = 0.2; kB = 0.2; deltaB = 0.1; Du1Dx = DuDx(1); %Du2Dx = DuDx(2); u1 = u(1); % u in my eqns u2 = u(2); % v in my eqns c = [1; 1]; f = [delta*Du1Dx-gamma*u1; 0] .* DuDx; F = -alpha*u1 + beta*u2; s = [F; muB*kB*u2^2/(kB^2+u2^2)-deltaB*u2-F];

% --------------------------------------------------------------------------

function u0 = pdex4ic(x) u0 = [1; 0];

% --------------------------------------------------------------------------

function [pl,ql,pr,qr] = pdex4bc(xl,ul,xr,ur,t) pl = [0; ul(2)]; ql = [1; 0]; pr = [ur(1)-1; 0]; qr = [0; 1];

Thank you so much for your attention.

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