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Analytical solutions of the nitrogen uptake model with Michaelis-Menten flux

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  • Lin, Wenting
  • Ning, Xin
  • Ou, Zhonghui

Abstract

In this paper, we describe the application of the generalized finite Hankel transform method to the convection diffusion problems of nitrogen in soil subject to Robin boundary conditions and the right-hand side of the left Robin boundary condition is the classic nonlinear Michaelis-Menten flux. If the Michaelis-Menten flux is taken as a function of time, the analytical solution of series form can be derived by the generalized finite Hankel transform. In the calculation, the Michaelis-Menten flux is evaluated by the numerical concentration at the root surface and the number of terms of the partial sum is determined after adequately approximating the numerical solution. Therefore, we improve and develop the analytical method built by Garg et al., and exemplify and verify it by the nitrogen uptake model for roots. The investigated model has a representatively and completely mathematical structure among most nutrient uptake models, and then the analytical method and the solutions developed here can also be used to nutrient uptake problems in soil subject to homogeneous or inhomogeneous Dirichlet or Neumann boundary conditions.

Suggested Citation

  • Lin, Wenting & Ning, Xin & Ou, Zhonghui, 2023. "Analytical solutions of the nitrogen uptake model with Michaelis-Menten flux," Applied Mathematics and Computation, Elsevier, vol. 438(C).
    • Handle: RePEc:eee:apmaco:v:438:y:2023:i:c:s0096300322006440
    DOI: 10.1016/j.amc.2022.127570
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    References listed on IDEAS

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    1. Mollier, Alain & De Willigen, Peter & Heinen, Marius & Morel, Christian & Schneider, André & Pellerin, Sylvain, 2008. "A two-dimensional simulation model of phosphorus uptake including crop growth and P-response," Ecological Modelling, Elsevier, vol. 210(4), pages 453-464.
    2. Zand-Parsa, Sh. & Sepaskhah, A.R. & Ronaghi, A., 2006. "Development and evaluation of integrated water and nitrogen model for maize," Agricultural Water Management, Elsevier, vol. 81(3), pages 227-256, March.
    3. Khader, M.M. & Sweilam, N.H., 2016. "Singularly perturbed BVP to estimation of diaphragm deflection in MEMS capacitive microphone: An application of ADM," Applied Mathematics and Computation, Elsevier, vol. 281(C), pages 214-222.
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