DAE Problem : cannot understand how to find the problem in my code

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Urvi 2012-9-28

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    This is code to solve 6 ode's and 12 algebraic equations. All of them are interdependent. How do I go about it? I keep getting errors but I am unable to solve it.     
**M file**
 *M file* function f=ncs1_dae(t,x)
          %Input parameters
          global alpha A AH AI AO AV ACS beta CPH CPI CPIN CPO CPV dB g hB hI hO hH hV Hmax k M MH min Pset qein R rhol rhov ri ro TIN TR vB lambda;
          input()
          %Variables
          TI=x(1);
........
..........
              =x(16);
          %f(1) to f(6) are ODEs
          f(1)=
          f(2)=
          f(3)=
          f(4)=
          f(5)=
          f(6)=
          %f(7) to f(18) are Algebraic Equations
          f(7)=
          f(8)=
          f(9)=
          f(10)=
          f(11)=
          f(12)=
          f(13)=
          f(14)=
          f(15)=
          f(16)=
          f(17)=
          f(18)=
          f=f';
          This is what I enter in the command window:
          >> x0=[298 298 298 298 1 0.3 0 373 0 0 0 0 0 0 0 0.0013 0.0041 0.0056];
          >> tspan=[0 1200];
          >> M=[eye(6,18);zeros(12,18)];
          >> options=odeset('Mass',M);
          >> [t1,x1]=ode15s(f,[0,1200],x0,options);
          The warning msg I get is : Warning: Failure at t=3.014342e-01. Unable to meet integration tolerances without reducing the step size below the smallest value allowed (8.881784e-16) at time t. > In ode15s at 753 >>    if true
                % code
              end

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Walter Roberson 2012-9-28

What if the equations are inconsistent?

Urvi 2012-10-1

Inconsistent as in? I have 18 variables and 18 equations. All of which are interdependent.

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Answer 1

Jan 2012-10-1

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编辑：Jan 2012-10-1

You can define an DAE such that there is no feasible point. If the mass matrix is singular, as in your case, the initial slope M(t0, y0) * y'(0) = f(t0, y0) must exist.

Imagine a DAE which describes a point sliding on a circulare wire. If you start the integration with a point apart from the wire, there is no valid first step of the integration, because it is impossible to keep the trajectory on the feasible path.