Numerical Solutions of the Fisher-Kolmogorov-Petrovsky-Piskunov Equation on the Abundance of Chlorophyll-a in the Ocean

Department of Mathematics, Faculty of Mathematics and Natural Sciences, Universitas Syiah Kuala, Banda Aceh 23111, Indonesia

^* e-mail: tarmiziusman@usk.ac.id

Abstract

Chlorophyll-a is a crucial parameter for enhancing primary productivity in the food chain, generated through photosynthesis, and plays a significant role in maintaining aquatic ecosystem balance. This study employs the Fisher-Kolmogorov-Petrovsky-Piskunov (Fisher-KPP) equation to analyze the dynamic patterns of chlorophyll-a abundance in the Strait of Malacca (SM). The Fisher-KPP equation is numerically solved using the finite difference method (FDM) with the Crank-Nicolson (CN) scheme to produce solutions in the form of time series graphs. Time series graphs are effective in visualizing periodically measured or observed data over time. The objective of this study is to numerically simulate chlorophyll-a abundance in SM by varying boundary conditions represented as vectors. The simulation is divided into two cases, each using boundary conditions derived from minimum and average chlorophyll-a data values at latitude 4.0625 °N for u(0, t) and latitude 5.3125 °N for u(L, t). Results from both cases indicate that the distribution pattern of chlorophyll-a abundance in SM fluctuates and follows trends similar to observed data, with mean absolute errors (MAE) of 0.0831 mg/l and 0.5633 mg/l, respectively. The findings suggest that the Fisher-KPP equation with CN scheme effectively describes and reproduces data comparable to observational data.