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