A linearized fourth-order compact ADI method for phytoplankton-zooplankton model arising in marine ecosystem

Mathematical models and numerical simulations have been prominently successful in providing insight for the exploration of evolution mechanism in scientific engineering. In this paper, a linearized fourth-order compact alternating direction implicit (ADI) method is developed to numerically solve a mathematical model, which includes phytoplankton-zooplankton interactions arising in marine ecosystem. The solvability, convergence and stability of the proposed method are discussed as well. It is proven that the proposed method is fourth-order accurate in space and second-order accurate in time. Finally, we present several numerical simulations to confirm the theoretical results.