Open AccessNumerical analysis of the Volterra differential equations via a combination of evolutionary algorithms with moving least squares and finite difference methods
Author(s) -
Mahmoodabadi Mohammad Javad
Publication year - 2021
Publication title -
the journal of engineering
Language(s) - English
Resource type - Journals
ISSN - 2051-3305
DOI - 10.1049/tje2.12024
Subject(s) - particle swarm optimization , mathematics , nonlinear system , least squares function approximation , evolutionary algorithm , differential equation , differential evolution , finite difference , mathematical optimization , finite difference method , algorithm , computer science , mathematical analysis , statistics , physics , quantum mechanics , estimator
In this paper, the Volterra differential equations governing on the predator‐prey dynamics is numerically solved through the combination of evolutionary algorithms with Moving Least Squares as well as the Finite Difference Method. Among the numerous evolutionary algorithms, the Genetic Algorithms and Particle Swarm Optimization, as two powerful and effective approaches, are selected. The penalty method is chosen to impose the initial conditions on the objective function, while the Moving Least Squares is implemented to interpolate the derivatives in the differential equations. In order to illustrate the effectiveness of the Moving Least Squares, the results are compared with those obtained via the Finite Difference Method based evolutionary algorithms. Moreover, the results are associated with those of a numerical method and an analytical scheme to evaluate the obtained populations of the prey and the predator. These comparisons clearly illustrate the reliability and efficiency of the proposed methodology to solve nonlinear differential equations.