Treatment of Stiff Initial Value Problems using Block Backward Differentiation formula

Abstract

Some Block Backward Differentiation Formulas (BDFs) capable of generating solutions to Stiff initial value problems are derived using Lagrangian interpolation technique. The region of absolute stability of the BDFs are constructed and the nature so obtained establishes some fact about the choice of BDFs for numerical treatment of stiff Problems. The BDFs derived were implemented on some standard stiff initial value Problems. The results show that the 3-point BDF step size ratio with r = 2 has the widest region of absolute stability and highest accuracy.

Keywords: Zero stability, Hybrid, k–step, Block methods, first order initial value problem