Stability Domains of Explicit Multistep Methods

IF 0.4 Q4 MATHEMATICS, APPLIED

Numerical Analysis and Applications Pub Date : 2022-12-08 DOI:10.1134/s1995423922040073

I. V. Kireev, A. E. Novikov, E. A. Novikov

引用次数: 0

Abstract

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.

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显式多步骤方法的稳定域

摘要提出了一种求解多步数值格式稳定域的新算法。该算法基于计算复系数多项式的最大数量级根的伯努利方法和计算平方根的Dandelin-Lobachevsky-Gräffe方法。给出了3-11阶Adams-Bashforth方法稳定域构造的数值结果。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Numerical Analysis and Applications MATHEMATICS, APPLIED-

CiteScore

1.00

自引率

0.00%

发文量

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.