Two Problems with NDSolve, Overflow and Projection method

Questions
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1

Hello
I tried to solve a system first order differential equations together with a constraint equation. I use the Method->Projection to check if the constraint holds at each step. However, two problems occur:

The messages:

General::ovfl: Overflow occurred in computation. and General::unfl: Underflow occurred in computation,

appear and I do not how to handle them.

The second problem occurs by the message:

NDSolve::nlnum: "The function value {Overflow[],Overflow[],Overflow[],Overflow[]} is not a list of numbers with dimensions {4} at {t,u[t],x[t],y[t],z[t]}...

I have attached the image of the code with the given explanations in (**) for convenience.

I would appreciate if any one give me a help.

My best regards Hadi

2

Replace

...
\[Theta]=0.182; w=0; \[Rho]i=4.2; xi=0.0; ui=8.71; adot= -6.4; zi=26.57; om=11.72; ti=0.0; ts=10000;
...
g = NDSolve[..., WorkingPrecision -> MachinePrecision]

with

...
\[Theta]=182/1000;w=0; \[Rho]i=42/10;xi=0;ui=871/100;adot= -64/10;zi=2657/100;om=1172/100;ti=0;ts=10000;
...
g = NDSolve[..., WorkingPrecision -> 64]
Plot[{x[t], x'[t], x''[t]} /. g[[1]], {t, 0, 29.16}]
Plot[{u[t], u'[t], y[t]} /. g[[1]], {t, 0, 29.16}]
Plot[{z[t]} /. g[[1]], {t, 0, 29.16}]

and the overflow problems are no longer reported, but

NDSolve::ndsz: At t == 29.1681...8`64., step size is effectively zero; singularity or stiff system suspected. >>

remains.

3

Hi Bill

Thanks for your help, it worked.

Best

Hadi