Integration failure in PDE system (N = 3)

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MG 2017-3-22

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https://ww2.mathworks.cn/matlabcentral/answers/331235-integration-failure-in-pde-system-n-3

评论： MG 2017-10-3

Hello,

I am working on a three-equations system, composed of two ODEs and one PDE. I have some external functions (containing time-dependent parameters), and two PDE coefficients (a and c) in functional form. The script correctly works with one pair of dimension/element size, but results are not reasonable because the problem is strongly mesh sensitive. So I tried to reduce the element dimension but I have this warning:

Warning: Failure at t=6.217997e+00.  Unable to meet integration tolerances without reducing the step
size below the smallest value allowed (1.421085e-14) at time t. 
> In ode15s (line 668)
  In pde.EquationModel/solveTimeDependent (line 83)
  In pde.PDEModel/solvepde (line 54)
  In pde3 (line 61) % This command is: results = solvepde(pdem, t);

that leads to the failure of the script.

Searching through the documentation, the problem seems the ode15 solver, which is automatically called by the solvepde(pdem, t) command.

I already tried to change tolerances as follow:

pdem.SolverOptions.RelativeTolerance = 1.0e-1;
pdem.SolverOptions.AbsoluteTolerance = 1.0e-1;
pdem.SolverOptions.ResidualTolerance = 1.0e-1;
pdem.SolverOptions.MaxIterations = 30;
pdem.SolverOptions.MinStep = 1.0e-20;

but it doesn't work.

How can I fix this problem?

Thank you