A Class of A-Stable Hybrid Block Backward Differentiation Formulae for Solving Stiff Chemical Reaction Problems of Ordinary Differential Equations

Abstract

A major challenge in simulating chemical reaction processes is integrating the stiff systems of Ordinary Differential Equations (ODEs) describing the chemical reactions due to stiffness. Thus, it would be of interest to search systematically for stiff solvers that are close to optimal for such problems. This paper presents an implicit 2-Step and 3-Step Hybrid Block Backward Differentiation Formulae with one off-step point in (2SHBBDF) and two off-step point in (3SHBBDF) for the solutions of first-order stiff chemical reaction problems. In deriving the methods, the polynomial basis function was adopted. The paper further analyses the basic properties of the (2SHBBDF) and (3SHBBDF) which include order of accuracy, consistence, zero-stability, convergence and the stability regions of the methods was also computed. To demonstrate the accuracy of the proposed approach, some famous stiff chemical reaction problems such as Robertson problem and Stiff Chemical reactions were solved, and the results obtained were compared with those of some existing methods. The results obtained clearly show that our new methods perform better than the existing methods with which we compared our results.