A new optimal multistep optimal homotopy asymptotic method to solve nonlinear system of two biological species

IF 2.4 Q2 ENGINEERING, MECHANICAL

Nonlinear Engineering - Modeling and Application Pub Date : 2023-01-01 DOI:10.1515/nleng-2022-0230

Z. Ayati, S. Pourjafar

{"title":"A new optimal multistep optimal homotopy asymptotic method to solve nonlinear system of two biological species","authors":"Z. Ayati, S. Pourjafar","doi":"10.1515/nleng-2022-0230","DOIUrl":null,"url":null,"abstract":"Abstract Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering. The aim of current study is to apply the well-known optimal homotopy asymptotic method (OHAM) on a specific and famous model of these equations. It is illustrated that auxiliary functions and the number of Taylor series terms affect the accuracy of the solution. Hence, at first a solution has been found with an acceptable error by OHAM. Then, it has been continued to attain a better solution by Multistep optimal homotopy asymptotic method. All these processes had improved the precision of the solution. Auxiliary polynomials of two, three, and four degrees and different numbers of Taylor series term have been investigated to solve a nonlinear system derived by two biological species ‎living together. Ultimately, appropriate results with auxiliary polynomials of degree four and Taylor series with six terms have been obtained precisely. In addition, the error values decrease significantly compared to the other cases.","PeriodicalId":37863,"journal":{"name":"Nonlinear Engineering - Modeling and Application","volume":"16 1","pages":""},"PeriodicalIF":2.4000,"publicationDate":"2023-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Nonlinear Engineering - Modeling and Application","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1515/nleng-2022-0230","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"ENGINEERING, MECHANICAL","Score":null,"Total":0}

引用次数: 0

Abstract

Abstract Recently solving integro-differential equations have been the focus of attention among many researchers in the field of mathematic and engineering. The aim of current study is to apply the well-known optimal homotopy asymptotic method (OHAM) on a specific and famous model of these equations. It is illustrated that auxiliary functions and the number of Taylor series terms affect the accuracy of the solution. Hence, at first a solution has been found with an acceptable error by OHAM. Then, it has been continued to attain a better solution by Multistep optimal homotopy asymptotic method. All these processes had improved the precision of the solution. Auxiliary polynomials of two, three, and four degrees and different numbers of Taylor series term have been investigated to solve a nonlinear system derived by two biological species ‎living together. Ultimately, appropriate results with auxiliary polynomials of degree four and Taylor series with six terms have been obtained precisely. In addition, the error values decrease significantly compared to the other cases.

查看原文本刊更多论文

求解两种生物非线性系统的一种新的最优多步最优同伦渐近方法

近年来，积分微分方程的求解一直是数学界和工程界研究的热点。本研究的目的是将著名的最优同伦渐近方法(OHAM)应用于这些方程的一个特定的著名模型。说明辅助函数和泰勒级数项的个数影响解的精度。因此，首先找到了一个具有可接受误差的解决方案。然后，利用多步最优同伦渐近方法得到了较好的解。所有这些过程都提高了溶液的精度。研究了二阶、三次和四次的辅助多项式和泰勒级数项的不同个数，以求解由两种生物共同生活的非线性系统。最后，精确地得到了四次辅助多项式和六项泰勒级数的适当结果。与其他情况相比，误差值明显减小。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Nonlinear Engineering - Modeling and Application Multiple-

CiteScore

6.20

自引率

3.60%

发文量

审稿时长

44 weeks

期刊介绍： The Journal of Nonlinear Engineering aims to be a platform for sharing original research results in theoretical, experimental, practical, and applied nonlinear phenomena within engineering. It serves as a forum to exchange ideas and applications of nonlinear problems across various engineering disciplines. Articles are considered for publication if they explore nonlinearities in engineering systems, offering realistic mathematical modeling, utilizing nonlinearity for new designs, stabilizing systems, understanding system behavior through nonlinearity, optimizing systems based on nonlinear interactions, and developing algorithms to harness and leverage nonlinear elements.