{"title":"Sixth-order compact difference scheme and multigrid method for solving the Poisson equation","authors":"","doi":"10.1007/s40096-023-00522-3","DOIUrl":null,"url":null,"abstract":"<h3>Abstract</h3> <p>This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second derivative. The biggest difference between the proposed scheme and other sixth-order scheme is that the right hand contains second partial derivation of source term; this term makes the proposed scheme more accurate than other sixth-order schemes. The proposed scheme is combined with the multigrid method to solve two- and three-dimensional Poisson equations with Dirichlet boundary conditions. The result is compared with other sixth-order schemes in several numerical experiments. The numerical results show that the proposed scheme achieves the desired accuracy and has smaller errors than other schemes of the same order. Further, the multigrid method is higher efficient than traditional iterative method in accelerating the convergence.</p>","PeriodicalId":48563,"journal":{"name":"Mathematical Sciences","volume":"65 1","pages":""},"PeriodicalIF":1.9000,"publicationDate":"2024-01-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Mathematical Sciences","FirstCategoryId":"100","ListUrlMain":"https://doi.org/10.1007/s40096-023-00522-3","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
This paper proposes a sixth-order compact difference scheme of Poisson equation based on the sixth-order compact difference operator of the second derivative. The biggest difference between the proposed scheme and other sixth-order scheme is that the right hand contains second partial derivation of source term; this term makes the proposed scheme more accurate than other sixth-order schemes. The proposed scheme is combined with the multigrid method to solve two- and three-dimensional Poisson equations with Dirichlet boundary conditions. The result is compared with other sixth-order schemes in several numerical experiments. The numerical results show that the proposed scheme achieves the desired accuracy and has smaller errors than other schemes of the same order. Further, the multigrid method is higher efficient than traditional iterative method in accelerating the convergence.
期刊介绍：
Mathematical Sciences is an international journal publishing high quality peer-reviewed original research articles that demonstrate the interaction between various disciplines of theoretical and applied mathematics. Subject areas include numerical analysis, numerical statistics, optimization, operational research, signal analysis, wavelets, image processing, fuzzy sets, spline, stochastic analysis, integral equation, differential equation, partial differential equation and combinations of the above.
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