{"title":"Efficient spectral methods for the fourth-order elliptic eigenvalue problems","authors":"Suna Ma , Huiyuan Li","doi":"10.1016/j.matcom.2024.12.006","DOIUrl":null,"url":null,"abstract":"<div><div>An efficient spectral-Galerkin method for eigenvalue problems of the fourth-order elliptic equation on the unit ball is proposed in this paper. The efficiency of the method lies in the use of properly designed ball polynomials as basis functions. Error estimates for numerical eigenvalues and eigenvectors are conducted for the original fourth-order elliptic eigenvalue problem rather than the equivalent one-dimensional eigenvalue problem based on the pole condition in the literature. Numerical experiments are shown to demonstrate the efficiency of the algorithm and to validate the theoretical results.</div></div>","PeriodicalId":49856,"journal":{"name":"Mathematics and Computers in Simulation","volume":"232 ","pages":"Pages 1-16"},"PeriodicalIF":4.4000,"publicationDate":"2025-06-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematics and Computers in Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S0378475424004774","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"2024/12/15 0:00:00","PubModel":"Epub","JCR":"Q1","JCRName":"COMPUTER SCIENCE, INTERDISCIPLINARY APPLICATIONS","Score":null,"Total":0}
引用次数: 0
Abstract
An efficient spectral-Galerkin method for eigenvalue problems of the fourth-order elliptic equation on the unit ball is proposed in this paper. The efficiency of the method lies in the use of properly designed ball polynomials as basis functions. Error estimates for numerical eigenvalues and eigenvectors are conducted for the original fourth-order elliptic eigenvalue problem rather than the equivalent one-dimensional eigenvalue problem based on the pole condition in the literature. Numerical experiments are shown to demonstrate the efficiency of the algorithm and to validate the theoretical results.
期刊介绍：
The aim of the journal is to provide an international forum for the dissemination of up-to-date information in the fields of the mathematics and computers, in particular (but not exclusively) as they apply to the dynamics of systems, their simulation and scientific computation in general. Published material ranges from short, concise research papers to more general tutorial articles.
Mathematics and Computers in Simulation, published monthly, is the official organ of IMACS, the International Association for Mathematics and Computers in Simulation (Formerly AICA). This Association, founded in 1955 and legally incorporated in 1956 is a member of FIACC (the Five International Associations Coordinating Committee), together with IFIP, IFAV, IFORS and IMEKO.
Topics covered by the journal include mathematical tools in:
•The foundations of systems modelling
•Numerical analysis and the development of algorithms for simulation
They also include considerations about computer hardware for simulation and about special software and compilers.
The journal also publishes articles concerned with specific applications of modelling and simulation in science and engineering, with relevant applied mathematics, the general philosophy of systems simulation, and their impact on disciplinary and interdisciplinary research.
The journal includes a Book Review section -- and a "News on IMACS" section that contains a Calendar of future Conferences/Events and other information about the Association.
京公网安备 11010802042870号
京ICP备2023020795号-1
分享
求助内容：
应助结果提醒方式：
扫码关注我们
