{"title":"求解一维Klein-Gordon方程的时空无网格方法","authors":"Zhiqiang Zhang, Fuzhang Wang, Juan Zhang","doi":"10.1051/wujns/2022274313","DOIUrl":null,"url":null,"abstract":"A simple direct space-time meshless scheme, based on the radial or non-radial basis function, is proposed for the one-dimensional Klein-Gordon equations. Since these equations are time-dependent, it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects. The first scheme is fulfilled by considering time variable as normal space variable, to construct an \"isotropic\" space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way. Numerical results show that the proposed meshless schemes are simple, accurate, stable, easy-to-program and efficient for the Klein-Gordon equations.","PeriodicalId":23976,"journal":{"name":"Wuhan University Journal of Natural Sciences","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2022-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations\",\"authors\":\"Zhiqiang Zhang, Fuzhang Wang, Juan Zhang\",\"doi\":\"10.1051/wujns/2022274313\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"A simple direct space-time meshless scheme, based on the radial or non-radial basis function, is proposed for the one-dimensional Klein-Gordon equations. Since these equations are time-dependent, it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects. The first scheme is fulfilled by considering time variable as normal space variable, to construct an \\\"isotropic\\\" space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way. Numerical results show that the proposed meshless schemes are simple, accurate, stable, easy-to-program and efficient for the Klein-Gordon equations.\",\"PeriodicalId\":23976,\"journal\":{\"name\":\"Wuhan University Journal of Natural Sciences\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2022-08-01\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Wuhan University Journal of Natural Sciences\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.1051/wujns/2022274313\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q3\",\"JCRName\":\"Multidisciplinary\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Wuhan University Journal of Natural Sciences","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.1051/wujns/2022274313","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"Multidisciplinary","Score":null,"Total":0}
The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations
A simple direct space-time meshless scheme, based on the radial or non-radial basis function, is proposed for the one-dimensional Klein-Gordon equations. Since these equations are time-dependent, it is worthwhile to present two schemes for the basis functions from radial and non-radial aspects. The first scheme is fulfilled by considering time variable as normal space variable, to construct an "isotropic" space-time radial basis function. The other scheme considered a realistic relationship between space variable and time variable which is not radial. The time-dependent variable is treated regularly during the whole solution process and the Klein-Gordon equations can be solved in a direct way. Numerical results show that the proposed meshless schemes are simple, accurate, stable, easy-to-program and efficient for the Klein-Gordon equations.
期刊介绍:
Wuhan University Journal of Natural Sciences aims to promote rapid communication and exchange between the World and Wuhan University, as well as other Chinese universities and academic institutions. It mainly reflects the latest advances being made in many disciplines of scientific research in Chinese universities and academic institutions. The journal also publishes papers presented at conferences in China and abroad. The multi-disciplinary nature of Wuhan University Journal of Natural Sciences is apparent in the wide range of articles from leading Chinese scholars. This journal also aims to introduce Chinese academic achievements to the world community, by demonstrating the significance of Chinese scientific investigations.