A-Stable Variable Step Size Super Class of Block Backward Differentiation Formula for the Numerical Integration of Stiff Initial Value Problems

Abstract

A new variable step size superclass of block backward differentiation formula (BBDF) for the numerical integration of stiff initial value problems (IVPs) is developed. The proposed method is of order five and is designed to compute two solution values simultaneously per step. The Stability analysis confirms that the method is both zero-stable and A-stable. Comparative numerical experiments with some existing schemes demonstrate that the new method delivers improved efficiency and accuracy. Hence, it offers a viable and effective alternative for solving both linear and nonlinear stiff IVPs.