Hello!

I am encountering some issues related to very small time steps in my numerical simulations and would appreciate your assistance.

In my model, the time step `dt`

is extremely small, approximately on the order of `10^-12`

. I am using the implicit difference method to handle the time derivative, and there are two ways to approach this:

Using `dt`

as a divisor (i.e., dividing the change in the variable by `dt`

).

Using `dt`

as a multiplier (i.e., multiplying other terms by dt so that the time difference term eliminates `dt`

).

I have a concern that using `dt`

as a multiplier will result in very small values in the matrix, which might affect the solution process. This is my own observation, and I am not sure if it is correct.

Most of the examples I have seen use `dt`

as a multiplier. However, given the very small time step in my model, I am worried that this approach may impact the computational accuracy and stability.

Could you please advise which method is recommended in this situation and why?

Thank you very much for your help!