A Variable Step Size Multi-Block Backward Differentiation Formula for Solving Stiff Initial Value Problem of Ordinary Differential Equations

Abstract

A variable step size multi-block backward differentiation formula for solving stiff initial value problems of ordinary differential equations with a variable step size strategy was derived. The proposed method (VSSMBBDF) computes two approximate solution values at a time per integration step. The stability properties are achieved by varying the step size ratio in the formula to generate more zero stable schemes. The proposed method is also found to be an A-Stable scheme across different choices of the step size. The method is capable of solving stiff IVPs of ODEs. Approximates result from the system of stiff ODE problems considered are found to favorably validate the performance of 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 method can be an alternative solver for stiff IVPs of ODEs.