MATLAB: Pdepe: why does spatial discretization fail

Question

Hi,

when trying to solve a PDE very similar to the heat equation pdepe yields the following:

>> pdetest
Error using pdepe (line 293)
Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.
Error in pdetest (line 5)
sol = pdepe(0,@pde,@pdeic,@pdebc,xmesh,tspan);

What am I missing here? Please see the used code below:

function pdetest
xmesh = linspace(-4,3,82);
tspan = linspace(0,1,12);
sol = pdepe(0,@pde,@pdeic,@pdebc,xmesh,tspan);
function [c,f,s] = pde(x,t,u,DuDx)
c = 1; 
f = 0.0968*DuDx;
s = 0; 
function u0 = pdeic(x)
xmesh = linspace(-4,3,82);
[~, index] = min(abs(xmesh-x));
initial_values = [0.3639 0.3720 0.3801 0.3884 0.3968 ...
0.4054 0.4141 0.4229 0.4319 0.4411 0.4504 0.4599 0.4696 ... 
0.4794 0.4894 0.4995 0.5098 0.5204 0.5310 0.5419 0.5530 ...
0.5642 0.5756 0.5873 0.5991 0.6111 0.6234 0.6358 0.6485 ...
0.6614 0.6745 0.6878 0.7014 0.7152 0.7292 0.7435 0.7580 ...
0.7727 0.7878 0.8030 0.8186 0.8344 0.8504 0.8668 0.8834 ...
0.9003 0.9175 0.9350 0.9528 0.9709 0.9893 1.0081 1.0271 ...
1.0465 1.0662 1.0863 1.1067 1.1274 1.1485 1.1700 1.1918 ...
1.2140 1.2366 1.2596 1.2829 1.3067 1.3309 1.3555 1.3805 ...
1.4059 1.4318 1.4581 1.4849 1.5121 1.5398 1.5680 1.5966 ...
1.6258 1.6554 1.6856 1.7163 1.7475];
u0 = initial_values(index);
function [pl,ql,pr,qr] = pdebc(xl,ul,xr,ur,t)
pl = 0.3639;
ql = 0; 
pr = 1.7475;
qr = 0;

Answer 1

I think you want the following in your pdebc function:

function [pl,ql,pr,qr] = pdebc(xl,ul,xr,ur,t)
pl = ul-0.3639;
ql = 0; 
pr = ur-1.7475;
qr = 0;