Second derivative off-node block adaptive backward differentiation formulae for stiff initial value problems

Abstract

The quest for more efficient schemes that handle stiff initial value problems (IVPs) has led to the emergence of new families of methods. Amongst these methods is the Adaptive Backward Differentiation Formula (A-BDF), which is a variant of the Backward Differentiation Formula (BDF). In this study, a family of Block Adaptive Backward Differentiation Formulae is considered and it is developed through Taylor series expansion and the method of undetermined coefficients. The methods constructed herein are of order p = 2k. Numerical experiments on standard test problems show that the proposed methods produced more accurate solutions than existing methods in the literature.