Analytical solution of Nye-Tinker-Barber model by Laplace transform
Yue Wang1, Wenting Lin1, Zhonghui Ou2
1College of Mathematics and Statistics, Fujian Normal University, Fuzhou, 350007, Fujian, PR China.
Bio Systems
|February 10, 2023
Summary
This study presents an accurate analytical solution for plant root nutrient uptake using the Nye-Tinker-Barber model. The novel approach enhances computational efficiency compared to existing numerical methods.
Area of Science:
- Plant Physiology
- Mathematical Modeling
- Soil Science
Background:
- The Nye-Tinker-Barber model describes nutrient uptake by plant roots.
- This model involves complex nonlinear boundary conditions, specifically the Michaelis-Menten function.
Purpose of the Study:
- To develop a more accurate and computationally efficient analytical solution for the Nye-Tinker-Barber model.
- To apply Laplace and Zakian inversion methods for solving nutrient uptake dynamics.
Main Methods:
- Numerical fitting of the Michaelis-Menten function to time-dependent root surface concentration.
- Application of Laplace and numerical inverse Laplace transforms using the Zakian inversion method.
- Comparison of the analytical solution with difference schemes and the Stehfest inversion method.
Main Results:
- An approximate analytical solution was obtained with higher accuracy and efficiency.
- The developed analytical method demonstrated superior performance over existing numerical and analytical techniques.
- The method shows promise for application to other nutrient uptake models.
Conclusions:
- The Laplace and Zakian inversion method provides an accurate and efficient analytical solution for nutrient uptake modeling.
- This approach offers a significant improvement over traditional numerical methods.
- The methodology is adaptable for broader applications in plant nutrient uptake research.
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