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

Yoshitaka Watanabe, Mitsuhiro T. Nakao

Research output: Contribution to journalArticle

3 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 languageEnglish
Pages (from-to)239-251
Number of pages13
JournalApplied Mathematics and Computation
Volume276
DOIs
Publication statusPublished - 2016 Mar 5
Externally publishedYes

Fingerprint

Numerical Verification
Functional equation
Nonlinear Equations
Computer-assisted Proof
Iteration
Nonlinear Partial Differential Equations
Partial differential equations
Differential equations
Differential equation
Form

Keywords

  • Differential equation
  • Functional equation
  • Newton-like iteration
  • Residual form

ASJC Scopus subject areas

  • Computational Mathematics
  • Applied Mathematics

Cite this

A numerical verification method for nonlinear functional equations based on infinite-dimensional Newton-like iteration. / Watanabe, Yoshitaka; Nakao, Mitsuhiro T.

In: Applied Mathematics and Computation, Vol. 276, 05.03.2016, p. 239-251.

Research output: Contribution to journalArticle

@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 = "3",
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

VL - 276

SP - 239

EP - 251

JO - Applied Mathematics and Computation

JF - Applied Mathematics and Computation

SN - 0096-3003

ER -