I am trying to solve a system of 3 PDEs using pdepe in MATLAB. But I am getting an error

Here is the code

    % 
function pdex51
m = 0;
x = 0:0.005:1;
t = 0:0.01:1;
options=odeset('Reltol',1e-10,'Abstol',1e-8);
sol = pdepe(m,@pdex5pde,@pdex5ic,@pdex5bc,x,t,options);
u1 = sol(:,:,1);
u2 = sol(:,:,2);
u3 = sol(:,:,3);
% --------------------------------------------------------------
function [c,f,s] = pdex5pde(x,t,u,DuDx)
A=1; Re=1; strainrate=1;
c = [1; 1; Re]; 
n=1.2;
alpha= [0; 1; strainrate].*DuDx ;
f=alpha;
f(1)=0;
f(2)= alpha(3);
f(3)= alpha(2);
s = [A; (-u(2)/(1+u(1)^n)); 0 ] + [ - strainrate*u(1) ;0 ; 0].*flipud(DuDx);
% --------------------------------------------------------------
function u0 = pdex5ic(x)
u0 = [0; 0;0]; 
% --------------------------------------------------------------
function [pl,ql,pr,qr] = pdex5bc(xl,ul,xr,ur,t)
pl = [0; 0; ul(3)]; 
ql = [1; 0;0]; 
pr = [0;0;ur(3)-1*heaviside(t-1e-15)]; 
qr = [1; 0;0];

Now I am getting the error "Error using daeic12 (line 77) This DAE appears to be of index greater than 1.

Error in ode15s (line 311) [y,yp,f0,dfdy,nFE,nPD,Jfac] = daeic12(odeFcn,odeArgs,t,ICtype,Mt,y,yp0,f0,...

Error in pdepe (line 317) [t,y] = ode15s(@pdeodes,t,y0,opts);

Error in pdex51 (line 6) sol = pdepe(m,@pdex5pde,@pdex5ic,@pdex5bc,x,t,options); " Please help me in this regard Thanks

Answer 1

[Torsten]

You don't supply boundary conditions for u(2).

This gives a singular matrix and is not allowed within pdepe.

Best wishes

Torsten.

[Rusty]

Thank you sir for your reply, Please have a look at my pde

now I am providing the vaue of the constants, i.e. A=1. n=1.2, gammaNaughtDot=1 and Re=1. But the problem is that I do not have any BC in u(2).

[Rusty]

And another thing I wanted to say that you ca replace u2 in the third eqn by substituting the value of u2 from the eqn 2. Now you do not have a derivative of u2 wrt to y . Then I think we do not need a BC. Please correct me if there is something wrong with this reasoning, Thanks

[Torsten]

Your equations don't belong to the class of equations that can be solved using pdepe (they don't contain 2nd order spatial derivatives). Thus you will have to discretize the equations in space on your own and use ODE15S to solve the resulting system of ordinary differential equations.

Best wishes

Torsten.

[Rusty]

cam you please elaborate on this, or give me some reference. Thanks

[Torsten]

E.g.

Schiesser: The numerical method of lines

or, if you have access to the NAG Toolbox, you can use

 http://www.nag.co.uk/numeric/MB/manual64_24_1/html/D03/d03plf.html

Best wishes

Torsten.

[Rusty]

Thank you sir