NUMERICAL SIMULATION FOR THE FRACTIONAL LAKE POLLUTION MODEL USING TWO ACCURATE NUMERICAL METHODS

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.