{"title":"同调分析方法与Clique多项式方法的研究","authors":"S. Kumbinarasaiah, P. PreethamM.","doi":"10.22034/CMDE.2021.46473.1953","DOIUrl":null,"url":null,"abstract":"This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Non-linear initial value problems are converted into non-linear algebraic equations by discretion with suitable grid points in the current approach. We solved highly non-linear initial problems using the (HAM) Homotopy analysis method and CPM. Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analyses are reflected in terms of the theorem.","PeriodicalId":44352,"journal":{"name":"Computational Methods for Differential Equations","volume":null,"pages":null},"PeriodicalIF":1.1000,"publicationDate":"2021-10-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"2","resultStr":"{\"title\":\"A Study on Homotopy Analysis Method and Clique Polynomial Method\",\"authors\":\"S. Kumbinarasaiah, P. PreethamM.\",\"doi\":\"10.22034/CMDE.2021.46473.1953\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Non-linear initial value problems are converted into non-linear algebraic equations by discretion with suitable grid points in the current approach. We solved highly non-linear initial problems using the (HAM) Homotopy analysis method and CPM. Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analyses are reflected in terms of the theorem.\",\"PeriodicalId\":44352,\"journal\":{\"name\":\"Computational Methods for Differential Equations\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-10-25\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"2\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Computational Methods for Differential Equations\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.22034/CMDE.2021.46473.1953\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q2\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Computational Methods for Differential Equations","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.22034/CMDE.2021.46473.1953","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q2","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A Study on Homotopy Analysis Method and Clique Polynomial Method
This paper generated the novel approach called the Clique polynomial method (CPM) using the Clique polynomials raised in graph theory. Non-linear initial value problems are converted into non-linear algebraic equations by discretion with suitable grid points in the current approach. We solved highly non-linear initial problems using the (HAM) Homotopy analysis method and CPM. Obtained results reveal that the present technique is better than HAM that is discussed through tables and simulations. Convergence analyses are reflected in terms of the theorem.
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