A New Fifth Order Variable Step Size Block Backward Differentiation Formula with Off-Step Points for the Numerical Solution of Stiff Ordinary Differential Equations

Abstract

A new fully implicit two point variable step size based on block backward differentiation formula with two off-step points for the numerical integration of first order stiff ordinary differential equations in initial value problems is proposed. The methods are derived by introducing three different values of the step size ratio to the existing fifth order 2-point block backward differentiation formula with off-step points for solving stiff ordinary differential equations. The methods approximate two solutions values with two off-step points simultaneously at each step of the integration in block. The order, error constant, and consistency of the methods are presented. The stability analysis of the methods indicates that the methods are both zero and A-stable. The proposed methods are implemented in Microsoft Dev C++ compiler using Newton’s iteration and the numerical comparison of results with existing algorithm of the same order shows that the proposed methods are better in terms of accuracy and compete with 3DIBBDF in terms of computation time. Hence, the proposed methods serve as alternative solver for stiff ODEs.