Sigularity problem in NDSolve in mathematica

In summary, the conversation discusses the singularity problem encountered while using the "NDSolve" function in mathematica to solve a set of 13 differential equations with boundary conditions constrained from experimental observations. The error "NDSolve::ndsz" is mentioned and possible causes such as an analytic singularity or a stiff system are discussed. Suggestions are given to check for these issues and to potentially non-dimensionalize the equations to improve the numerical integration.
  • #1
sigularity problem in "NDSolve" in mathematica


I am trying to solve numerically 13 differential equations with intial boundary conditions in mathematica. In my case, the boundary conditions are not free parameters and those are constrained from experimental observations.
But these set of equations and boundary condition give the error in NDSolve as following,

"NDSolve::ndsz: At e == 11.706899882374666`, step size is effectively zero; singularity or stiff system suspected. >>"

Because of this error, the plots of those 13 variables changes abruptly at "e == 11.706899882374666`".
I am getting nice curve upto this particular vaue of "e".

My question is , How can get nice curve even after this value without changing the boundary conditions?

Thanks in advance,
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  • #2
Check for the two issues the error mentions.

Examine your diff eq's for evidence of an analytic singularity if you can. Maybe check limiting behaviors too.

If you can rule that out around the troubled value for e, then it might be the stiff system case.

If the numerical integration is rapidly oscillating between large numbers, it's not going to compute properly and the errors are going to propagate hugely. Try to nondimentionalize your equations and make sure the order of magnitude of your constants are similar if you can. If there are too many different time and length-scales in your system, it might not be able to be numerically solved this way.

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