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

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))];

Answer 1

[Bill Greene]

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,~)

[Mallikarjuna M]

Thank you sir it worked