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 func-tion.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.

ZHANG Zhiqiang;WANG Fuzhang;ZHANG Juan

General Education Center,Zhengzhou Business University,Gongyi 451200,Henan,China;School of Mathematics and Statistics,Xuzhou University of Technology,Xuzhou 221018,Jiangsu,China;School of Computer Science&Technology,Huaibei Normal University,Huaibei 235000,Anhui,China;School of Information and Control Engineering,China University of Mining and Technology,Xuzhou 221116,Jiangsu,China

武汉大学自然科学学报（英文版）

[1]ZHANG Zhiqiang;WANG Fuzhang;ZHANG Juan-.The Space-Time Meshless Methods for the Solution of One-Dimensional Klein-Gordon Equations)[J].武汉大学自然科学学报（英文版）,2022(04):313-320

Space,Time,Meshless,Methods,Solution,One,Dimensional,Klein,Gordon,Equations,simple,direct,space,meshless,radial,basis,proposed,one,dimensional,equations,Since,these,are,dependent,it,worthwhile,present,two,schemes,functions,from,aspects,first,fulfilled,by,considering,variable,normal,construct,isotropic,other,considered,realistic,relationship,between,which,not,treated,regularly,during,whole,solution,process,can,solved,way,Numerical,results,show,that,accurate,stable,easy,program,efficient

0.508169