- #1

maistral

- 240

- 17

In the paper:

**(Celaya, et al); I have found this formula:**

*Implementation of an Adaptive BDF2 Formula and Comparison with the MATLAB Ode15s*It's supposed to be a local truncation error formula which compares the numerical solution y

_{n+2}to that of a Taylor expansion y(t

_{n+2}). While I can set the values of h to be equal with each other (thus retrieving the constant step version), I have no idea how to derive this term if I want to bring it to higher orders (say, I want a fourth-order solution which would den require the calculation of a fifth derivative term with variable stepsize).

TLDR: Does anyone know how this thing has been made? I have been scouring the internet for a while about this and I seem to have no information as to how this thing appeared (I mean, looking at the four papers I have now, this just magically appeared).

Thanks!