Long-time stability and convergence of a BDF3 method for a parabolic equation with fading memory

arXiv:2610.32364v1 Announce Type: new Abstract: We analyze the long-time stability and convergence of a third-order backward differentiation formula (BDF3) for parabolic equations with exponentially fading memory. The BDF3 scalar resolvent has oscillatory coefficients, so the monotonicity argument used for lower-order formulas in [Math. Comp. 62 (1994) 477-496] does not apply. We instead control memory feedback by the absolute mass of its discrete Green sequence and establish the rigorous stability-constant bounds $23/20