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- How do I start BDF iterations? Any suggestions?

As we know, backward differentiation formulas for ODE start off with the backward Euler; which proceeds as:

If I wanted to switch to the second order method;

Can anyone recommend me ideas as to how to generate the initially required y

If I wanted to switch to the second order method;

Can anyone recommend me ideas as to how to generate the initially required y

_{n+1}? The only thing I can think of are as follows:- Use a standard Runge-Kutta to generate the second point, but in my opinion this is somehow futile as the reason why we use implicit methods is to avoid the instabilities which will generated via a standard explicit approach (like Runge-Kutta).
- Use the backward Euler technique with some microscopic (lol) stepsizes to assure that I am accurate, then I switch to a higher BDF method? Say, I want to propagate a second-order solution with a stepsize of 0.1. Maybe I should generate a backward Euler solution of step 0.001? Or something?