{"title":"Analytic Method for Solving One Class of Nonlinear Equations","authors":"Yu. S. Popkov","doi":"10.1134/S1064562424601392","DOIUrl":null,"url":null,"abstract":"<p>An analytical approximate method for calculating multidimensional integrals of analytic functions is proposed, in which the integrand is approximated by a power series. This approach transforms the original system of nonlinear equations with integral components into a system of equations with a polynomial left-hand side. To solve equations of this class, an analytical method based on abstract power series is developed. A recurrent procedure is developed for the analytical solution of this class of nonlinear equations.</p>","PeriodicalId":531,"journal":{"name":"Doklady Mathematics","volume":"110 2","pages":"404 - 407"},"PeriodicalIF":0.6000,"publicationDate":"2024-11-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Doklady Mathematics","FirstCategoryId":"100","ListUrlMain":"https://link.springer.com/article/10.1134/S1064562424601392","RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q3","JCRName":"MATHEMATICS","Score":null,"Total":0}
引用次数: 0
Abstract
An analytical approximate method for calculating multidimensional integrals of analytic functions is proposed, in which the integrand is approximated by a power series. This approach transforms the original system of nonlinear equations with integral components into a system of equations with a polynomial left-hand side. To solve equations of this class, an analytical method based on abstract power series is developed. A recurrent procedure is developed for the analytical solution of this class of nonlinear equations.
期刊介绍：
Doklady Mathematics is a journal of the Presidium of the Russian Academy of Sciences. It contains English translations of papers published in Doklady Akademii Nauk (Proceedings of the Russian Academy of Sciences), which was founded in 1933 and is published 36 times a year. Doklady Mathematics includes the materials from the following areas: mathematics, mathematical physics, computer science, control theory, and computers. It publishes brief scientific reports on previously unpublished significant new research in mathematics and its applications. The main contributors to the journal are Members of the RAS, Corresponding Members of the RAS, and scientists from the former Soviet Union and other foreign countries. Among the contributors are the outstanding Russian mathematicians.
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