Convergence and order of the diagonally implicit extended 3-point super class of block backward differentiation formula for stiff initial value problems

Abstract

This study investigates the convergence properties of the diagonally implicit extended 3-point superclass block backward differentiation formula (DIE3SBBDF) developed by Yusuf et al. (2026) for the numerical solution of stiff initial value problems. The convergence of the method is established by analyzing its consistency and zero-stability properties. The order of accuracy of the method is also determined, and the method is shown to be of fifth order. These results provide a theoretical basis for the convergence and accuracy of the DIE3SBBDF method in solving first-order stiff initial value problems.