Is there any systemic way of determining a better guess while solving DAEs using ODE15s?

When running the attached code (or code on the dropbox link):

https://www.dropbox.com/s/7sz6gli891k0u4l/simultaneousEquations1.m?dl=0

I get the error message:

"Error using daeic12 (line 166) Need a better guess y0 for consistent initial conditions.

Error in ode15s (line 310) [y,yp,f0,dfdy,nFE,nPD,Jfac] = daeic12(odeFcn,odeArgs,t,ICtype,Mt,y,yp0,f0,...

Error in simultaneousEquations1 (line 79) [t,y] = ode15s(@(ti,yi)revisedModelode(ti,yi),tspan,y0,options);

>> "

Is there any systemic way of determining a better guess?

[Torsten]

Did you correct your equations ?

[Dursman Mchabe]

Hello Torsten, I have checked the equations, at this stage I con not see the mistake yet, probably because I developed them. However the original equations were taken from two papers:

(1) https://pubs.acs.org/doi/abs/10.1021/ie9709446 Equations 41 to 50.

(2) https://www.sciencedirect.com/science/article/pii/S0378382010002547 Equations 1 to 54.

It usually takes me a while to spot my own mistakes. However I'm also trying different approaches as well. E.g. I have split the set of equations into two:

(a) I solve 7 unknowns from 7 ODEs (ODE45).

(b) Then I also solve 9 unknowns from 9 algebraic (fsolve).

The equations are solved in time-steps. Nine variables (taken from fsolve solution) are kept as constant parameters while solving the differential equations. Similarly, 7 variables from ODE45 is used as input constant parameters in the next time step of the fsolve. The loop continues like that.

I am currently doing it manually, and comparing the outcome with the experimental results.

I hope I will be able to loop the two functions using matlab.

[Torsten]

At least one mistake must be that from equations (15) and (16) it follows that y(4)=y(5).

[Torsten]

To get consistent initial values for your DAE system, simply solve the 9 algebraic equations with the 7 values for the differential variables fixed and equal to y0(1),...,y0(7) using "fsolve".

This will give you y0(8),...,y0(16).

Best wishes

Torsten.

[Dursman Mchabe]

Thanks a lot Torsten. That simplifies my work a lot.

[Star Strider]

Torsten is the acknowledged expert on the differential equation solvers amongst the MATLAB Answers Contributors.

Answer 1

[Haritha]

Try this,

https://in.mathworks.com/help/matlab/math/choose-an-ode-solver.html

[Dursman Mchabe]

Thanks Haritha, I will revisit that.