On the Newton–Kantorovich Scheme for Evolutionary Equations

Abstract We propose a constructive form of the Newton–Kantorovich method to obtain solutions for evolutionary equations with small nonlinearities. The construction is applicable to equations in non-Banach linear spaces. The paper presents only a sketch of the method, without specifying the norms involved and without giving necessary $$\varepsilon$$ – $$\delta$$ details.

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Publication Details

Journal
Proceedings of the Steklov Institute of Mathematics
Published
2024-12-01
DOI
https://doi.org/10.1134/s0081543824060063
Primary Topic
Stability and Controllability of Differential Equations
Type
article
Field-Weighted Citation Impact
0.00

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article

On the Newton–Kantorovich Scheme for Evolutionary Equations

Sergei B. Kuksin, Andrey Dymov
Proceedings of the Steklov Institute of Mathematics
Stability and Controllability of Differential Equations
article

On the Newton–Kantorovich Scheme for Evolutionary Equations

Sergei B. Kuksin, Andrey Dymov
article en

Abstract

Abstract We propose a constructive form of the Newton–Kantorovich method to obtain solutions for evolutionary equations with small nonlinearities. The construction is applicable to equations in non-Banach linear spaces. The paper presents only a sketch of the method, without specifying the norms involved and without giving necessary $$\varepsilon$$ – $$\delta$$ details.

Proceedings of the Steklov Institute of MathematicsVol. 327(1)
National Research University Higher School of Economics (RU), Peoples' Friendship University of Russia (RU), Centre National de la Recherche Scientifique (FR), Russian Academy of Sciences (RU), Shandong University (CN), Université Paris Cité (FR), Steklov Mathematical Institute (RU), Sorbonne Université (FR), Sorbonne Paris Cité (FR)
Ministry of Science and Higher Education of the Russian Federation
Openalex Percentile: Top 63%
Stability and Controllability of Differential Equations
DOIOpen Access PDFOpenAlex
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On the Newton–Kantorovich Scheme for Evolutionary Equations — Sergei B. Kuksin, Andrey Dymov · Proceedings of the Steklov Institute of Mathematics (2024) | TGRS Research Map | TGRS