Say, I have a system \dot{u} = f(u(t),t). I want to linearize the RHS at u(t_{n}) and have \dot{u} = f(u(t_n),t_n) + f_{u}'(u(t_n),t_n)\cdot(u(t)-u(t_{n})).

In terms of DifferentialEquations.jl I can define `f(u,p,t)`

where `u`

corresponds to u(t). How can I pass `u_n`

obtained at the previous step to `f(u,p,t)`

?

That’s just a specific time stepper and not well-defined as a differential equation. I’m not 100% sure what you’re trying to ask.

I want to do the following:

- Fix timestep h, and
`t_(n+1) = t_n + h`

- Linearize the RHS at
`u_n`

- Solve linearized eq for
`u_(n+1)`

The linearized RHS depends explicitly on `u_n`

, which is basically a parameter which is obtained at the previous step. Using DiffEq interface, is it possible to update this parameter using a callback or anything else? In other words, take the result of the previous step and pass it to `f(u,p,t)`

at the current step.