Numerical Solutions of Stiff Chemical Reaction Problems using Hybrid Block Backward Differentiation Formula

This research paper introduces an advanced approach to address the numerical challenges associated with stiff chemical reaction problems. We propose employing a Hybrid Diagonally Implicit Block Backward Differentiation Formula coupled with strategically placed off-step points to improve the accuracy and efficiency of numerical solutions. Stiff chemical reactions, commonly encountered in various industrial processes, require advanced numerical techniques to precisely capture rapid changes in concentrations. Our hybrid formulation enhances stability and computational efficiency by building on the diagonally implicit structure of block backward differentiation formulas, offering improved performance for solving stiff chemical reaction problems. Under a specific selection of a free parameter, the method is found to possess both zero-stability and A−stability properties. Convergence analysis demonstrates its ability to accurately approximate exact solutions. Through rigorous experimentation and comparative analysis, this research will illustrate the effectiveness of the developed method in solving stiff ordinary differential equations. The expected outcomes include the development of the new numerical method, its validation through comprehensive numerical experiments and insights into its performance and applicability in diverse science and engineering domains.