{"title":"双曲电报方程的新解","authors":"Mohammad Partohaghighi, M. Akinlar, G. Weber","doi":"10.3934/jdg.2020029","DOIUrl":null,"url":null,"abstract":"We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.","PeriodicalId":42722,"journal":{"name":"Journal of Dynamics and Games","volume":"1 1","pages":""},"PeriodicalIF":1.1000,"publicationDate":"2021-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":"{\"title\":\"New solutions of hyperbolic telegraph equation\",\"authors\":\"Mohammad Partohaghighi, M. Akinlar, G. Weber\",\"doi\":\"10.3934/jdg.2020029\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.\",\"PeriodicalId\":42722,\"journal\":{\"name\":\"Journal of Dynamics and Games\",\"volume\":\"1 1\",\"pages\":\"\"},\"PeriodicalIF\":1.1000,\"publicationDate\":\"2021-01-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"3\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Journal of Dynamics and Games\",\"FirstCategoryId\":\"1085\",\"ListUrlMain\":\"https://doi.org/10.3934/jdg.2020029\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Journal of Dynamics and Games","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.3934/jdg.2020029","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
We present a new method based on unification of fictitious time integration (FTI) and group preserving (GP) methods. The GP method is applied in numerically discretized ordinary differential equations obtained from application of FTI method to a given partial differential equation (PDE). The algorithm is applied to hyperbolic telegraph equation and utilizes the Cayley transformation and the Pade approximations in the Minkowski space. It avoids unauthentic solutions and ghost fixed points which is one of the advantages of the present method over other related numerical methods in the literature. The technique is tested on three specific examples for various parameter values appearing in the telegraph equation and discretization steps. Such solutions of the telegraph equation are obtained first time in this paper. Illustrative figures are provided. Efficiency of the method is determined by an error analysis which is achieved by comparing numerical solutions with exact solutions.
期刊介绍:
The Journal of Dynamics and Games (JDG) is a pure and applied mathematical journal that publishes high quality peer-review and expository papers in all research areas of expertise of its editors. The main focus of JDG is in the interface of Dynamical Systems and Game Theory.