3‑Point block backward diferentiation formula with an of‑step point for the solutions of stif chemical reaction problems

Soomro, Hira and Zainuddin, Nooraini and Daud, Hanita and Sunday, Joshua and Jamaludin, Noraini and Abdullah, Abdullah and Mulono, Aprianto and Kadir, Evizal Abdul (2022) 3‑Point block backward diferentiation formula with an of‑step point for the solutions of stif chemical reaction problems. Journal of Mathematical Chemistry, 61. pp. 75-97. ISSN 02599791

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Abstract

A major challenge in simulating chemical reaction processes is integrating the stif systems of Ordinary Diferential Equations (ODEs) describing the chemical reactions due to stifness. Thus, it would be of interest to search systematically for stif solvers that are close to optimal for such problems. This paper presents an implicit 3-Point Block Backward Diferentiation Formula with one of-step point (3POBBDF) for the solutions of irst-order stif chemical reaction problems. In deriving the method, the Lagrange polynomial was adopted as the basis function. The paper further analyses the basic properties of the 3POBBDF which include order of accuracy, consistence, zero-stability, and convergence. The stability region as well as the interval of instability of the method was also computed. To demonstrate the accuracy of the proposed approach, some famous stif chemical reaction problems such as Robertson problem and Chemical AKZO were solved, and the results obtained were compared with those of some existing methods. The results obtained clearly show that the 3POBBDF performs better than the existing methods with which we compared our results.

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