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Computer-Assisted Proofs for a Nonli...

Duchesne, Gabriel Willam,

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Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere /

Record Type:	Electronic resources : Monograph/item
Title/Author:	Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere // Gabriel Willam Duchesne.
Author:	Duchesne, Gabriel Willam,
Description:	1 electronic resource (101 pages)
Notes:	Source: Masters Abstracts International, Volume: 82-10.
Contained By:	Masters Abstracts International82-10.
Subject:	Computers. -
Online resource:	https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28265719
ISBN:	9798708703279

Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere /
Duchesne, Gabriel Willam,

Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere /Gabriel Willam Duchesne. - 1 electronic resource (101 pages)

Source: Masters Abstracts International, Volume: 82-10.

In this study, we prove the existence and local uniqueness of radially symmetric solutions of nonlinear partial differential equations via a rigorous numerical method. We introduce the concepts of Banach spaces of geometrically decaying sequences and explore the domains of convergence of the Taylor and Chebyshev expansions. These notions constitute the basis for the Radii Polynomial Theorem on Banach spaces of infinite sequences, which is the main tool employed to obtain the proofs by using a combination of Taylor and Chebyshev coefficients of the solutions. We also introduce briefly the notions of interval analysis to justify the rigor of our computer-assisted results.

English

ISBN: 9798708703279Subjects--Topical Terms:

544777
Computers.
Subjects--Index Terms:

Banach spaces

Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere /
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100 1 $a Duchesne, Gabriel Willam, $e author. $3 3823788
245 1 0 $a Computer-Assisted Proofs for a Nonlinear Laplace-Beltrami Equation on the Sphere / $c Gabriel Willam Duchesne.
264 1 $a Ann Arbor : $b ProQuest Dissertations & Theses, $c 2019
300 $a 1 electronic resource (101 pages)
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
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500 $a Source: Masters Abstracts International, Volume: 82-10.
500 $a Advisors: Lessard, Jean-Philippe.
502 $b M.Sc. $c McGill University (Canada) $d 2019.
520 $a In this study, we prove the existence and local uniqueness of radially symmetric solutions of nonlinear partial differential equations via a rigorous numerical method. We introduce the concepts of Banach spaces of geometrically decaying sequences and explore the domains of convergence of the Taylor and Chebyshev expansions. These notions constitute the basis for the Radii Polynomial Theorem on Banach spaces of infinite sequences, which is the main tool employed to obtain the proofs by using a combination of Taylor and Chebyshev coefficients of the solutions. We also introduce briefly the notions of interval analysis to justify the rigor of our computer-assisted results.
520 $a Dans cette etude, nous prouvons l'existence et l'unicite locale de solutions d'EDPs non lineaires et symetriques via une methode numerique. Nous introduisons des concepts sur les espaces de Banach de suites a decroissance geometrique et explorons les domaines de convergence des series de Taylor et de Chebyshev. Ces notions constituent les bases du Theoreme du Polynome de Rayons sur les espaces de Banach de suites infinies, qui sera l'outil principal pour obtenir les preuves en utilisant une combinaison de coefficients de Taylor et de Chebyshev. Nous introduisons egalement des notions de base sur l'analyse d'intervalle pour justifier la rigueur des resultats obtenus numeriquement.
546 $a English
590 $a School code: 0781
650 4 $a Computers. $3 544777
650 4 $a Applied mathematics. $3 2122814
650 4 $a Partial differential equations. $3 2180177
650 4 $a Banach spaces. $3 579190
653 $a Banach spaces
653 $a Partial differential equations
690 $a 0364
710 2 $a McGill University (Canada). $e degree granting institution. $3 3759190
720 1 $a Lessard, Jean-Philippe $e degree supervisor.
773 0 $t Masters Abstracts International $g 82-10.
790 $a 0781
791 $a M.Sc.
792 $a 2019
856 4 0 $u https://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=28265719