Journal of Advances in Applied Mathematics

Download PDF (410.4 KB) PP. 143 - 148 Pub. Date: October 15, 2019

DOI: 10.22606/jaam.2019.44002

• Kuiyuan Li^*
  Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA
• Josaphat Uvah
  Department of Mathematics and Statistics, University of West Florida, Pensacola, FL 32514, USA

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.

Steady-state diffusion, time stages, homotopy continuation.

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