A semi-analytical solution of stiff equations arising in chemistry problems by homotopy analysis method

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发表日期：

2025年1月25日

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K. N. Sachin,
Devi K. Suguntha,
S. Kumbinarasaiah

摘要

In chemistry, particularly in the context of chemical kinetics, reaction dynamics, or when modeling systems involving complex reactions or transport phenomena, stiff equations arise frequently. These are systems of ordinary differential equations (ODEs) that exhibit very different timescales for various components of the solution, making them challenging to solve numerically. A stiff equation is one where there are some components of the solution that change very rapidly compared to others. These rapid changes can cause numerical instability when using standard solvers unless the time step is made extremely small. This research investigates applying the homotopy analysis method (HAM) and Haar wavelet transform (HWT) to resolve the complex, stiff equations encountered in chemical problems. The HAM approach involves constructing $m^\textrm{th}$ $m^{th}$ -order deformation equations using an auxiliary function and a parameter. This iteration process collectively yields a semi-analytical solution. Similarly, the HWT is employed to transform the stiff differential equations into a system of algebraic equations that can be more efficiently solved. The study evaluates the effectiveness and accuracy of these HAM and HWT methods in addressing the high complexity and challenge of solving stiff chemical equations using traditional numerical techniques. The findings demonstrate that the proposed approaches offer a reliable and fast-converging solution. The performance of the HAM and HWT methods is illustrated through numerical examples, and the solutions are compared with Exact solutions and the Taylor wavelet method from the literature, with the efficiency represented using tables and figures.