Solving One Species Lotka–volterra Equation by the New Iterative Method (NIM)

Q3 Mathematics

WSEAS Transactions on Mathematics Pub Date : 2023-05-10 DOI:10.37394/23206.2023.22.38

B. Batiha

引用次数: 1

Abstract

In this paper, we investigate the use of the new iterative method, referred to as the NIM, for solving the one species LotkaVolterra equation. This equation, which describes the dynamics of populations in ecological systems, has been widely studied in the field of mathematical biology. However, finding an analytical solution to this equation can be challenging. To overcome this, we propose using the NIM as an alternative method for solving the equation. To demonstrate the effectiveness of the NIM, we conduct a comparative study between it and other wellestablished techniques such as the differential transformation method (DTM), the variational iteration method (VIM), and the Adomian decomposition method (ADM). Through numerical simulations, we show that the NIM is able to accurately and efficiently solve the one species LotkaVolterra equation, making it a promising tool for researchers in the field of mathematical biology.

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用新迭代法求解一类Lotka-volterra方程

在本文中，我们研究了一种新的迭代方法，称为NIM，用于求解单种群Lotka-Volterra方程。这个方程描述了生态系统中种群的动态，在数学生物学领域得到了广泛的研究。然而，找到这个方程的解析解可能很有挑战性。为了克服这一点，我们建议使用NIM作为求解方程的替代方法。为了证明NIM的有效性，我们将其与其他成熟的技术进行了比较研究，如微分变换法（DTM）、变分迭代法（VIM）和Adomian分解法（ADM）。通过数值模拟，我们表明NIM能够准确有效地求解单种群Lotka-Volterra方程，使其成为数学生物学领域研究人员的一个有前途的工具。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

WSEAS Transactions on Mathematics Mathematics-Discrete Mathematics and Combinatorics

CiteScore

1.30

自引率

0.00%

发文量

期刊介绍： WSEAS Transactions on Mathematics publishes original research papers relating to applied and theoretical mathematics. We aim to bring important work to a wide international audience and therefore only publish papers of exceptional scientific value that advance our understanding of these particular areas. The research presented must transcend the limits of case studies, while both experimental and theoretical studies are accepted. It is a multi-disciplinary journal and therefore its content mirrors the diverse interests and approaches of scholars involved with linear algebra, numerical analysis, differential equations, statistics and related areas. We also welcome scholarly contributions from officials with government agencies, international agencies, and non-governmental organizations.