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feat: start integrate-and-fire model #30

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@alexfikl alexfikl commented Oct 2, 2023

This implements a simple implicit L1 method for integrate-and-fire methods with a condition that's state dependent, i.e. $\text{if } c(t, y) > 0 \text{ then } y \gets g(t, y)$.

In general, it's meant for some sort of discontinuous functions where we don't have to guess the discontinuity. Still needs a bit of work to nail down the interface

  • How to update the time step better?
    • Right now it just does t += dt, which is obviously not enough. We need to see when the condition is set and save that time instead.
    • Could update [tnext, ynext] = advance(tnext, ynext) in case the advance function wants to change the time step?
  • How to handle the exponential model case?
    • In the case, it seems like solving the implicit equation just fails when we get close to the reset condition, so we can't use it as a reliable result.
    • How to set the next time step in that case?
  • Add tests
  • Add examples
  • Add documentation / changelog entries / etc.

@alexfikl alexfikl marked this pull request as draft October 2, 2023 13:43
@alexfikl alexfikl closed this Nov 22, 2023
@alexfikl alexfikl deleted the integrate-and-fire branch November 22, 2023 08:19
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