Two–Point Diagonally Implicit Extended Super Class of Block Backward Differentiation Formula for Stiff Initial Value Problems

Abstract

In this paper, a diagonal form of the extended super class of block backward differentiation formula is derived. The method is fully implicit and approximates two solution values at a time. By varying a parameter 𝜌𝜖 (–1,1) in the formula, different sets of formulae can be generated. Analysis of the method indicated that the method is both zero and A–stable, hence, suitable for solving stiff initial value problems. Comparison of the method with some existing algorithms showed its advantage in terms of accuracy over some methods.