Modified second derivative backward differentiation formulas with recursively nested hybrid evaluations

Abstract

A class of variable order second derivative backward differentiation formula with recursive hybrid evaluationis presented. The modified second derivative backward differentiation formula with recursively nested hybrid evaluation(MBDFRHE) is A-stable for step number k = 1(1)5, circumventing the Dahlquist second order barrier and the Daniel–Moore conjecture for A-stable linear multistep methods.