PDEtoolbox_Error using daeic3 (line 230) Need a better guess y0 for consistent initial conditions.

Hello,

I am trying to solve a system with three partial differential equations coupled by using PDE toolbox.

As I simulate my code, I keep getting an error, saying

Error using daeic3 (line 230)

Need a better guess y0 for consistent initial conditions.

I cannot figure out where the error comes from. Can anyone help me to figure out what the problem is?

Attached PDF file is equations and corresponding code that I am trying to solve.

Any help would be very much appreciated.

Also, let me know if I could provide more information regarding this.

Answer 1

[Ravi Kumar]

You do have a singula mass matrix becuase of the equation 2. If I understand correctly equation 1 can be solved in isolation. Once you have u1, can you attempt to solve equation 2 and 3 using u1? This may or may not resolve the issue, it will simplify the system a bit.

[Minjun Bae]

Good afternoon,

Thank you so much for the feedback.

My equation 2, which has been modified a little bit, is that

Since state.u(1,:) returns to a matrix with scalar value,

it is my understanding that I cannot use gradient function because it will return 1) gradient wrt x only.

So I defined the equation 2 as below:

(coefficients except f was set to 0)

[[function fmatrix = fcoeffunction(location,state)

.....

fmatrix(2,:) = E_over + I_tkns*(state.ux(1,:).*state.ux(2,:)+state.uy(1,:).*state.uy(2,:))/denom

where denom is defined as

denom = sqrt(state.ux(1,:).^2+state.uy(1,:).^2);]]

I ran the simulation again, and I got the error saying

Error using daeic3, this DEA appears to be of index greater than 1.

I believe that error also comes up when I have a singular matrix (?).

Do you think it is possible for you to identify what the problem is?

Thank you so much for your support.

[Ravi Kumar]

Can you attach the complete code that produces the error? Reproduction could would help identify any workaround.

[Minjun Bae]

Hello,

Please see the attached pdf file. I have included two function handles as well as my main code.

Thank you so much!

Best regards,