{"title":"显式多步骤方法的稳定域","authors":"I. V. Kireev, A. E. Novikov, E. A. Novikov","doi":"10.1134/s1995423922040073","DOIUrl":null,"url":null,"abstract":"<h3 data-test=\"abstract-sub-heading\">Abstract</h3><p>A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on the Bernoulli method for computing the greatest in magnitude root of polynomials with complex coefficients and the Dandelin–Lobachevsky–Gräffe method for squaring roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.</p>","PeriodicalId":43697,"journal":{"name":"Numerical Analysis and Applications","volume":"4 1","pages":""},"PeriodicalIF":0.4000,"publicationDate":"2022-12-08","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Stability Domains of Explicit Multistep Methods\",\"authors\":\"I. V. Kireev, A. E. Novikov, E. A. Novikov\",\"doi\":\"10.1134/s1995423922040073\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<h3 data-test=\\\"abstract-sub-heading\\\">Abstract</h3><p>A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on the Bernoulli method for computing the greatest in magnitude root of polynomials with complex coefficients and the Dandelin–Lobachevsky–Gräffe method for squaring roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.</p>\",\"PeriodicalId\":43697,\"journal\":{\"name\":\"Numerical Analysis and Applications\",\"volume\":\"4 1\",\"pages\":\"\"},\"PeriodicalIF\":0.4000,\"publicationDate\":\"2022-12-08\",\"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/s1995423922040073\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q4\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Numerical Analysis and Applications","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.1134/s1995423922040073","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
A new algorithm is proposed for obtaining stability domains of multistep numerical schemes. The algorithm is based on the Bernoulli method for computing the greatest in magnitude root of polynomials with complex coefficients and the Dandelin–Lobachevsky–Gräffe method for squaring roots. Numerical results on the construction of stability domains of Adams–Bashforth methods of order 3–11 are given.
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.
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