Numerical Solutions of the Fisher-Kolmogorov-Petrovsky-Piskunov Equation on the Abundance of Chlorophyll-a in the Ocean Tarmizi Usman, Muhammad Ikhwan, Amelia Sari
Department of Mathematics, Universitas Syiah Kuala
Abstract
Chlorophyll\(-\)a is a key parameter in enhancing primary productivity in the food chain generated through the photosynthesis process, which has significant implications in maintaining the balance of aquatic ecosystems. In this study, the Fisher\(-\)Kolmogorov\(-\)Petrovsky\(-\)Piskunov equation (Fisher\(-\)KPP) will be used to determine the dynamics of chlorophyll\(-\)a abundance in the Malacca Strait. The Fisher\(-\)KPP equation will be numerically solved using the finite difference method with the Crank\(-\)Nicholson scheme, yielding time series graph solutions. Time series graphs are effective visualizations for displaying periodically measured or observed data over time. This research aims to obtain numerical simulations of chlorophyll\(-\)a abundance in the Malacca Strait. Numerical simulations will vary boundary conditions represented as vectors. The simulations will be divided into two different cases, each using boundary conditions derived from the minimum and average values of chlorophyll\(-\)a data with latitude 4.065 North and 5.3125 North for boundary condition. Results from both cases show fluctuations in chlorophyll\(-\)a distribution in the Malacca Strait, following relatively similar trends to observed data patterns, with mean absolute errors (MAE) of 0.0831 and 0.5633 in each case, respectively. Based on the simulation results, it can be concluded that the Fisher\(-\)KPP equation with the Crank-Nicholson scheme effectively describes and produces data similar to observational data in this case study.
