A New Multi - Block Super Class of BDF for Integrating First Order Stiff IVP of ODEs

Abstract

A new multi-block super class of backward differentiation formula for integrating first order stiff IVPs with a variable mesh size strategy is derived. The proposed scheme approximate two solution values at a time per integration step. The stability properties are achieved by varying the mesh size ratio in the formula to generate more zero stable and A-Stable schemes, capable of solving stiff IVPs of ODEs. Approximates result from the system of stiff ODE problems considered are found to favorably validate the new method in terms of accuracy of the scale error and less executional time in respect to the two methods compared in the study. Hence, the proposed scheme can be used for solving for stiff IVPs of ODEs.