An efficient wavelet-based optimization algorithm for the solutions of reaction-diffusion equations in biomedicine. (April 2020) - Mahalakshmi, M.; Hariharan, G.; Brindha, G.R.
Highlights: A mathematical model of nonlinear reaction-diffusion equation in a solid of planar and spherical shape is discussed. An efficient wavelet-based spectral method has been developed for the analytical expressions pertaining to substrate concentration for all parameter values. The efficiency of the proposed wavelet method is confirmed using the computational CPU time. The proposed wavelet-based results are compared with Adomian Decomposition Method (ADM). Satisfactory agreement with ADM results is observed. Abstract: In this paper, a mathematical model of nonlinear reaction-diffusion equation with Michaelis–Menten kinetics in a solid of planar and spherical shape is discussed. The proposed model is based on non-stationary diffusion equation containing a non-linear term related to Michaelis–Menten kinetics of the enzymatic reaction. An efficient wavelet-based spectral method has been developed for the analytical expressions pertaining to substrate concentration for all parameter values. The efficiency of the proposed wavelet method is confirmed by mean of the computational CPU time. The proposed wavelet-based results are compared with Adomian Decomposition Method (ADM). Satisfactory agreement with ADM results is observed. Moreover, the use of the wavelet method is found to be simple, efficient, flexible, and straight forward. Also, it requires less computation costs.