A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Yoshitaka Watanabe; Mitsuhiro T. Nakao

doi:10.1016/j.amc.2015.12.021

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

Yoshitaka Watanabe^*, Mitsuhiro T. Nakao

^*この研究の対応する著者

研究成果: Article › 査読

6 被引用数 (Scopus)

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This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.

本文言語	English
ページ（範囲）	239-251
ページ数	13
ジャーナル	Applied Mathematics and Computation
巻	276
DOI	https://doi.org/10.1016/j.amc.2015.12.021
出版ステータス	Published - 2016 3月 5
外部発表	はい

ASJC Scopus subject areas

計算数学
応用数学

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10.1016/j.amc.2015.12.021

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abstract = "This paper describes a numerical verification of solutions for infinite-dimensional functional equations based on residual forms and Newton-like iteration. The method is based upon a verification method previously developed by the authors. Several computer-assisted proofs for differential equations, including nonlinear partial differential equations, are presented.",

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A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

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