{"title":"Criteria of Solvability for Asymmetric Difference Schemes at High-Accuracy Approximation of Boundary Conditions","authors":"V. I. Paasonen","doi":"10.1134/s1995423924030066","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>In this paper we study a technology of calculating difference problems with internal boundary conditions of flux balance constructed by means of one-sided multipoint difference analogs of first derivatives of arbitrary order of accuracy. The technology is suitable for any type of differential equations to be solved and admits the same type of realization at any order of accuracy. In contrast to the approximations based on an extended system of equations, this technology does not lead to complications in splitting multidimensional problems into one-dimensional ones. Sufficient conditions of solvability and stability are formulated for realizations of the algorithms by using the double-sweep method for boundary conditions of arbitrary order of accuracy. Their proof is based on a reduction of the multipoint boundary conditions to a form that does not violate the tridiagonal structure of the matrices and the establishment of conditions of diagonal dominance in the transformed matrix rows corresponding to the external and internal boundary conditions.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"39 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2024-09-13","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423924030066","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
引用次数: 0
Abstract
In this paper we study a technology of calculating difference problems with internal boundary conditions of flux balance constructed by means of one-sided multipoint difference analogs of first derivatives of arbitrary order of accuracy. The technology is suitable for any type of differential equations to be solved and admits the same type of realization at any order of accuracy. In contrast to the approximations based on an extended system of equations, this technology does not lead to complications in splitting multidimensional problems into one-dimensional ones. Sufficient conditions of solvability and stability are formulated for realizations of the algorithms by using the double-sweep method for boundary conditions of arbitrary order of accuracy. Their proof is based on a reduction of the multipoint boundary conditions to a form that does not violate the tridiagonal structure of the matrices and the establishment of conditions of diagonal dominance in the transformed matrix rows corresponding to the external and internal boundary conditions.
期刊介绍：
Numerical Analysis and Applications is the translation of Russian periodical Sibirskii Zhurnal Vychislitel’noi Matematiki (Siberian Journal of Numerical Mathematics) published by the Siberian Branch of the Russian Academy of Sciences Publishing House since 1998.
The aim of this journal is to demonstrate, in concentrated form, to the Russian and International Mathematical Community the latest and most important investigations of Siberian numerical mathematicians in various scientific and engineering fields.
The journal deals with the following topics: Theory and practice of computational methods, mathematical physics, and other applied fields; Mathematical models of elasticity theory, hydrodynamics, gas dynamics, and geophysics; Parallelizing of algorithms; Models and methods of bioinformatics.
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
