MATLAB: I am using the pdepe function and the question is how I could fix the following error: ‘This DAE appears to be of index greater than 1’.

Question

function modelo

m = 0;

r=20;

s=20;

x = linspace(0,1,r);

t = linspace(-0.3555,4,s);

sol = pdepe(m,@modelopde,@modeloic,@modelobc,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')

return

end

function [c,f,s] = modelopde(x,t,u,DuDx)

alpha = 1e-3;

c = [0;1];

f = [-u(1);0]+ alpha*DuDx;

a = 1048.92;

b = -0.1397;

ceq = u(2)/(a-b*u(2));

st = 21.57;

aux1=(-u(1)+ceq)*st;

aux2=(u(1)-ceq)*st;

s =[aux1;aux2];

return

end

function u0 = modeloic(x)

u0 = [4.47;2000/(0.1*(1-0.26))];

return

end

function [pl,ql,pr,qr] = modelobc(xl,ul,xr,ur,t)

pl = [ul(1)-4.47;0];

ql = [0; 0];

pr = [0; 0];

qr = [0; 0];

return

end

Errors:

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 modelo (line 9)

sol = pdepe(m,@modelopde,@modeloic,@modelobc,x,t);

Answer 1

You only prescribe one boundary condition for your PDE system, but four are necessary to fix the solution.

Best wishes

Torsten.