Numerical simulation for the treatment of nonlinear predator-prey equations by using the finite element optimization method

Date

2021

Authors

Srivastava, H.M.
Khader, M. M.

Journal Title

Journal ISSN

Volume Title

Publisher

Fractal and Fractional

Abstract

This article aims to introduce an efficient simulation to obtain the solution for a dynamical– biological system, which is called the Lotka–Volterra system, involving predator–prey equations. The finite element method (FEM) is employed to solve this problem. This technique is based mainly upon the appropriate conversion of the proposed model to a system of algebraic equations. The resulting system is then constructed as a constrained optimization problem and optimized in order to get the unknown coefficients and, consequently, the solution itself. We call this combination of the two well-known methods the finite element optimization method (FEOM). We compare the obtained results with the solutions obtained by using the fourth-order Runge–Kutta method (RK4 method). The residual error function is evaluated, which supports the efficiency and the accuracy of the presented procedure. From the given results, we can say that the presented procedure provides an easy and efficient tool to investigate the solution for such models as those investigated in this paper.

Description

Keywords

Lotka-Volterra system, finite element method (FEM), optimization technique, residual error function, fourth-order Runge-Kutta method (RK4 method), numerical simulations

Citation

Srivastava, H. M. & Khader, M. M. (2021). “Numerical simulation for the treatment of nonlinear predator-prey equations by using the finite element optimization method.” Fractal and Fractional, 5(2), 56. https://doi.org/10.3390/fractalfract5020056