{"title":"一阶方法稳定性多项式设计的数值算法","authors":"E. Novikov, M. V. Rybkov, A. Novikov","doi":"10.3384/ECP17142979","DOIUrl":null,"url":null,"abstract":"The algorithm for coefficients determination for stability polynomials of degree up to m = 35 is developed. The coefficients correspond to explicit Runge-Kutta methods of the first accuracy order. Dependence between values of a polynomial at the points of extremum and both size and form of a stability domain is shown. Numerical results are given.","PeriodicalId":56990,"journal":{"name":"建模与仿真(英文)","volume":null,"pages":null},"PeriodicalIF":0.0000,"publicationDate":"2018-12-19","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Numerical Algorithm for Design of Stability Polynomials for the First Order Methods\",\"authors\":\"E. Novikov, M. V. Rybkov, A. Novikov\",\"doi\":\"10.3384/ECP17142979\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"The algorithm for coefficients determination for stability polynomials of degree up to m = 35 is developed. The coefficients correspond to explicit Runge-Kutta methods of the first accuracy order. Dependence between values of a polynomial at the points of extremum and both size and form of a stability domain is shown. Numerical results are given.\",\"PeriodicalId\":56990,\"journal\":{\"name\":\"建模与仿真(英文)\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":0.0000,\"publicationDate\":\"2018-12-19\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"建模与仿真(英文)\",\"FirstCategoryId\":\"1093\",\"ListUrlMain\":\"https://doi.org/10.3384/ECP17142979\",\"RegionNum\":0,\"RegionCategory\":null,\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"\",\"JCRName\":\"\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"建模与仿真(英文)","FirstCategoryId":"1093","ListUrlMain":"https://doi.org/10.3384/ECP17142979","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"","JCRName":"","Score":null,"Total":0}
Numerical Algorithm for Design of Stability Polynomials for the First Order Methods
The algorithm for coefficients determination for stability polynomials of degree up to m = 35 is developed. The coefficients correspond to explicit Runge-Kutta methods of the first accuracy order. Dependence between values of a polynomial at the points of extremum and both size and form of a stability domain is shown. Numerical results are given.