Work

Numerical Simulation for the Fractional Lake Pollution Model Using Two Accurate Numerical Methods

Year: 2025

Type: article

Abstract: This paper introduces a novel simulation approach that employs Caputo and Caputo–Fabrizio fractional derivative operators to explore the solution behavior of the fractional pollution model for a network of three lakes jointed by canals. Two input models are addressed by leveraging a purportedly innovative approximation techniques based on Gegenbauer wavelet polynomials (GWPs) and fractional Simpson’s 1/3 rule (FSR). The spectral collocation method (SCM), leveraging the distinctive properties of GWPs are utilized to convert the model under consideration into a set of algebraic equations. The measurement of the residual error function (REF) confirms the precision and efficacy of the SCM. Additionally, for the second method, a numerical simulation of the resulting system of fractional integral equations (FIEs) is carried out using the FSR. Comparative analysis with the Runge–Kutta fourth-order method (RK4M) highlights the efficacy of the techniques developed to simulate the solution behavior of such models, offering simple and efficient simulation tools.

Source: Fractals

DOI: 10.1142/s0218348x25402650

Authors: M. ADEL, M. M. KHADER, N. H. SWEILAM, W. M. ABDELFATTAH

Institutions: Islamic University of Madinah, Imam Mohammad ibn Saud Islamic University, Cairo University, Zagazig University, University of Business and Technology

Language: English

Topic: Fractional Differential Equations Solutions

Subfield: Modeling and Simulation

Field: Mathematics

Domain: Physical Sciences

SDG: Clean water and sanitation

Open Access status: hybrid

Funder: Deanship of Scientific Research, Imam Mohammed Ibn Saud Islamic University