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Optimizing ODE solver performance for very small step size

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Angshuman Podder
Angshuman Podder 2021-2-21
编辑： Angshuman Podder 2021-2-23
Hi, I have a function (containing 2 diff. eqns) that needs to be solved. Unfortunately, the time step needed is 1e-11. I think the program will run into a memory issue. Is there any way to save values at a certain time interval? OR Do I need to non-dimensionalize the eqns.?
P.S. I am using the ode45 solver.
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J. Alex Lee
J. Alex Lee 2021-2-23
Not knowing details, the first thing I would always look at is if the problem can be nondimensionalized to remove units and more easily uncover stiffness. Especially since the plots shown have such huge orders of magnitude.
Angshuman Podder
Angshuman Podder 2021-2-23
编辑：Angshuman Podder 2021-2-23
I am sorry about that. Convergence is not the right word, it should be stability. For e.g the diameter/number density is going negative.
I think the ODEs are stiff. I just saw that there are ODE solvers for stiff eqns. Thanks again @Jan.
@J. Alex Lee, you are right. I will sit down with non-dimensionalizing the equations.

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