College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350007, Fujian, PR China.
College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350007, Fujian, PR China; Fujian Key Laboratory of Mathematical Analysis and Applications, Center of Applied Mathematics (FJNU), Fuzhou, 350007, Fujian, PR China.
Biosystems. 2023 Mar;225:104845. doi: 10.1016/j.biosystems.2023.104845. Epub 2023 Feb 9.
The Nye-Tinker-Barber model is a classical convection-diffusion model for nutrient uptake by plant roots in cylindrical coordinates and has one nonlinear left Robin boundary condition with Michaelis-Menten function of concentration. First the Michaelis-Menten function is fitted into a function of time by numerical concentration at root surface from difference scheme, and then the Laplace and numerical inverse Laplace transforms - Zakian inversion method are taken to obtain the approximate analytical solution. Compared with other solutions made by difference scheme, Stehfest inversion method and previous analytical methods, it is found that the analytical solution obtained by Laplace and Zakian inversion transforms has higher accuracy and computation efficiency. This analytical method can be extended to other nutrient uptake models with Michaelis-Menten function.
奈廷格尔-巴伯模型是一个经典的圆柱坐标下植物根系养分吸收的对流扩散模型，具有一个非线性左罗宾边界条件和米氏-门坦函数浓度。首先，通过差分格式从根表面的数值浓度拟合米氏-门坦函数为时间的函数，然后采用拉普拉斯变换和数值反拉普拉斯变换-扎金反演方法得到近似解析解。与差分格式、斯特夫特反演方法和先前的解析方法得到的其他解相比，发现拉普拉斯和扎金反演变换得到的解析解具有更高的精度和计算效率。这种解析方法可以扩展到具有米氏-门坦函数的其他养分吸收模型。
