Pdepe: Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.

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i am trying to solve the diffusion reaction using pdepe but it is showing an error like
Spatial discretization has failed. Discretization supports only parabolic and elliptic equations, with flux term involving spatial derivative.
any problem with the boundary. x(0)=1,x'(1)=0, y(1)=1,x'(0)=0
function steady
m = 0;
x = linspace(0,1);
t = linspace(0,1000);
sol = pdepe(m,@pdex4pde,@pdex4ic,@pdex4bc,x,t);
u1 = sol(:,:,1);
%u2= sol(:,:,2);
%figure
plot(x, u1(end,:),'b')
hold on
%title('u1(x, t)')
%xlabel('Distance x')
%ylabel('u1(x,t)')
%figure
%plot(x, u2(end,:),'b')
%title('u2(x, t)')
%figure
% --------------------------------------------------------------
function [c,f,s] = pdex4pde(~,~,u,DuDx)
al=0.1;phi=0.0009;
c = [1;1];
f = [1;1].* DuDx;
F1=-9.*phi.^2.*(u(1)./1+u(1)+u(2));
F2=-9.*al.^2.*(u(2)./1+u(1)+u(2));
s = [F1;F2];
% --------------------------------------------------------------
function u0 = pdex4ic(~)
u0 = [0; 1];
% --------------------------------------------------------------
function [pl,ql,pr,qr] = pdex4bc(~,~,ul,ur,~)
%bi=10.0;
pl = [ul(1)-1;0];
ql = [0;1];
pr = [0;ur(2)-1];
qr = [1;0];
%qr = [0; bi*(1-ur(2))];

Accepted Answer

Bill Greene
Bill Greene on 8 Feb 2022
Your definition of the input arguments for the boundary condition function is incorrect.
Replace,
function [pl,ql,pr,qr] = pdex4bc(~,~,ul,ur,~)
with
function [pl,ql,pr,qr] = pdex4bc(xl,ul,xr,ur,t)
or
function [pl,ql,pr,qr] = pdex4bc(~,ul,~,ur,~)

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