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

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

5 Citations (Scopus)

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.

Original language	English
Pages (from-to)	239-251
Number of pages	13
Journal	Applied Mathematics and Computation
Volume	276
DOIs	https://doi.org/10.1016/j.amc.2015.12.021
Publication status	Published - 2016 Mar 5
Externally published	Yes

Keywords

Differential equation
Functional equation
Newton-like iteration
Residual form

ASJC Scopus subject areas

Computational Mathematics
Applied Mathematics

Access to Document

10.1016/j.amc.2015.12.021

Cite this

@article{093e71737f76457b98de1d2cc0851696,

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

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.",

keywords = "Differential equation, Functional equation, Newton-like iteration, Residual form",

author = "Yoshitaka Watanabe and Nakao, {Mitsuhiro T.}",

year = "2016",

month = mar,

day = "5",

doi = "10.1016/j.amc.2015.12.021",

language = "English",

volume = "276",

pages = "239--251",

journal = "Applied Mathematics and Computation",

issn = "0096-3003",

publisher = "Elsevier Inc.",

}

TY - JOUR

T1 - A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration

AU - Watanabe, Yoshitaka

AU - Nakao, Mitsuhiro T.

PY - 2016/3/5

Y1 - 2016/3/5

N2 - 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.

AB - 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.

KW - Differential equation

KW - Functional equation

KW - Newton-like iteration

KW - Residual form

UR - http://www.scopus.com/inward/record.url?scp=84952803254&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84952803254&partnerID=8YFLogxK

U2 - 10.1016/j.amc.2015.12.021

DO - 10.1016/j.amc.2015.12.021

M3 - Article

AN - SCOPUS:84952803254

SN - 0096-3003

VL - 276

SP - 239

EP - 251

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

ER -

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

Abstract

Keywords

ASJC Scopus subject areas

Access to Document

Other files and links

Fingerprint

Cite this