Numerical and Stability Investigations of the Waste Plastic Management Model in the Ocean System

Abstract

This study investigates the solution of an ocean waste plastic management system model. The model is represented by a nonlinear system which is divided into three compartments: the waste plastic materials W(τ), marine debris M(τ), and the process of recycling R(τ). These compartments form a simulated model that is solved using two collocation techniques based on a shifted version of the Morgan-Voyce (MV) functions, while the first matrix collocation procedure is directly applied to the given model, in the second approach we fuse the technique of quasilinearization together with the shifted MV (SMV) collocation strategy. Moreover, we give the basic reproduction number and discuss the existence of equilibria and the local stability of equilibria are investigated. The basic definitions of the SMV polynomials are introduced and detailed convergence analysis of the related power series expansion in both weighted L2 and L∞ norms are presented. Diverse numerical simulations are performed to prove the accurateness and effectiveness of the presented approaches and the results ate illustrated through tables and figures.