Question: Help setting inequality constraints where the right hand side is different than 0

[AaronHKim]

I am interested in using CVode to integrate with inequality constraints where the right-hand side is different than zero, e.g., y_1 < 5. What is the intended method for doing this? Should I be modifying my states so that the inequality constraint changes, i.e., change y_1 = y_1 - 5 so that the new inequality constraint is y_1 <0, or is there a different method that I can use instead? I would like to avoid modifying my states if possible.

Additionally is there some intended method of implementing a 2-sided band constraint, where a<=y<=b?

[balos1]

This was answered on the SUNDIALS mailing list.

Hello Kim Aaron,

Yes, to solve that problem with CVODE will have to
make a change of variables from y_i to y_i - bound
in order to enforce a bound y_i < bound.

-Alan H

[AaronHKim]

Thank you for the reply!

Do you happen to know of any additional information on the second question regarding how to implement a 2-banded constraint where a<=y<=b?

Edit (answered by mailing list):

As with the upper bound question, CVODE has no built-in
constraint option of that type. Here is how you can do it:
In addition to changing variables from y to y-b and requiring this variable to be <= 0, add to the system another dependent variable z which is equal to y-a,
have z satisfy the same ODE that y does (with the shift accounted for in its right-hand side function), and require the constraint z >= 0. The two resulting numerical solutions for y will agree within specified tolerances.

In any case, please be aware that if the true solution of the ODE system takes y outside of that band, CVODE cannot resolve that conflict, and will grind to a halt. If the true solution does indeed stay in the band, any actual numerical violations of the bounds (detected internally), will be temporary and will be corrected by CVODE.

-Alan H