Selvi M Salai Mathi, Hariharan G, Kannan K
Department of Mathematics, School of Humanities and Sciences, SASTRA University, Thanjavur, Tamilnadu, 613 401, India.
J Membr Biol. 2017 Dec;250(6):663-670. doi: 10.1007/s00232-017-0001-z. Epub 2017 Nov 17.
A mathematical model of a reaction-diffusion within an entrapped-cell photobioreactor packed with gel granules containing immobilized photosynthetic bacterial cells is discussed. A theoretical model is based on a system of coupled nonlinear reaction-diffusion equations. In this research work, we have developed an efficient wavelet-based spectral approach for solving the proposed model. Analytical expressions for the concentration of substrate and product are established for all values of reaction-diffusion parameters using second kind Chebyshev wavelet method. The analytical results were also compared with Homotopy perturbation method (HPM) and Adomian decomposition method (ADM). Satisfactory agreement with ADM and HPM solutions is observed. Moreover, the use of Chebyshev wavelets is found to be simple, reliable, efficient, and computationally attractive.
讨论了一种固定化细胞光生物反应器内的反应扩散数学模型，该反应器填充有包含固定化光合细菌细胞的凝胶颗粒。理论模型基于耦合非线性反应扩散方程组。在本研究工作中，我们开发了一种基于小波的高效谱方法来求解所提出的模型。使用第二类切比雪夫小波方法，针对反应扩散参数的所有值建立了底物和产物浓度的解析表达式。还将解析结果与同伦摄动法（HPM）和阿当分解法（ADM）进行了比较。观察到与ADM和HPM解具有令人满意的一致性。此外，发现使用切比雪夫小波简单、可靠、高效且在计算上具有吸引力。
