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Journal of Advances in Applied Mathematics
JAAM > Volume 4, Number 4, October 2019

Mathematical Methods for Dissolved Phosphorus Concentrations

Download PDF  (410.4 KB)PP. 143-148,  Pub. Date:September 29, 2019
DOI: 10.22606/jaam.2019.44002

Author(s)
Kuiyuan Li, Josaphat Uvah
Affiliation(s)
Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
Abstract
Phosphorus is a nutrient contained in fertilizer that can run off from lawns and crops. Predicting the phosphorus concentrations is an important component in determining how phosphorus is cycled in the surrounding ecosystem. In this paper, we present the development of two mathematical methods. The first is a steady-state diffusion ordinary differential equation with given initial data. For this method, we estimate the unknown parameter values using least squares approximations for the data set without the boundary values. The second method is identical to the first except that the boundary values are imposed. We then distinguish our methods from existing approaches by deploying homotopy continuation to connect all time stages. With this approach, phosphorus concentrations can be estimated at all times and any depth. Using real-life data, we give an example to show that the methods are not only easy to use, but also provide estimates between any time stages and at any depth.
Keywords
Steady-state diffusion, time stages, homotopy continuation.
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