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5-Point Block Backward Differentiation Formulae for Solving Stiff Chemical Reaction Problems of Ordinary Differential Equations

Samson Yunusa, Imande Terdon Terlumun,, Etuk Emmanuel Dan, and Micah Michael

Abstract

The development and application of a 5-Point Block Backward Differentiation Formula (5PBBDF) for the numerical solution of stiff ordinary differential equations , with an emphasis on issues related to chemical reaction kinetics, is presented in this paper. Numerical techniques with exceptional stability properties are required for stiff systems, which are frequently found in combustion modeling and reactive flow simulations. These systems are characterized by solution components that evolve on radically different timescales. By using a block formulation that concurrently computes numerical solutions at five equally spaced points, the suggested method expands upon the traditional Backward Differentiation Formula . By lowering the number of matrix factorizations needed throughout the integration interval, this block approach improves computational efficiency. A variable step-size strategy is used in its implementation to strike a balance between computational cost and local error control. The method is derived with specific coefficients optimized for both accuracy and stability. The A-stability of the 5PBBDF, which makes it especially appropriate for stiff systems, is confirmed by analyzing its stability using linear stability theory. Numerical experiments on common stiff chemical reaction problems, such as the Robertson chemical kinetics problem and a model combustion system, are used to assess the method's performance. The 5PBBDF is a reliable and effective solver for stiff ODEs in chemical engineering applications because numerical results show that it achieves better accuracy and computational efficiency than explicit methods.

Keywords

Stiff Chemical ReactionLinear Multistep MethodBlock MethodBackward Differentiation Formulae and ODEs. MSC 2020 Subject Classification Number: 34A1265L0465L0565L0665L2080A30

References

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