Approximate analytical solution of non-linear reaction-diffusion equations in a cubic-autocatalytic reaction with Michaelis–Menten decay

V. Ananthaswamy, S. Narmatha
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Abstract

The mathematical model pertaining to the cubic-autocatalytic reaction with M-M decay considered in one- dimensional reaction-diffusion cell is discussed. Approximate analytical solutions have been derived for the concentrations of the reactant and autocatalyst in the steady state and the non-steady state using the Homotopy analysis method. When the decay is linear, the model becomes the standard Gray-Scott model, and the corresponding approximate analytical solutions are also derived. The derived analytical expressions are compared with the numerical results with the help of MATLAB and are found to make a very good fit for small values of parameters.
具有Michaelis-Menten衰变的三次自催化反应非线性扩散方程的近似解析解
讨论了一维反应扩散池中具有M-M衰变的立方自催化反应的数学模型。用同伦分析方法导出了稳态和非稳态下反应物和自催化剂浓度的近似解析解。当衰减为线性时,模型成为标准的Gray-Scott模型,并推导出相应的近似解析解。在MATLAB软件的帮助下,将导出的解析表达式与数值结果进行了比较,发现对于较小的参数值具有很好的拟合性。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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