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Solutions of Quasilinear PDEs in Bal...

Chen, Zhengqin.

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.

Record Type:	Electronic resources : Monograph/item
Title/Author:	Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.
Author:	Chen, Zhengqin.
Published:	Ann Arbor : ProQuest Dissertations & Theses, 2017
Description:	178 p.
Notes:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Notes:	Adviser: Scott R. Fulton.
Contained By:	Dissertation Abstracts International79-02B(E).
Subject:	Applied mathematics.
Online resource:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10605390
ISBN:	9780355241259

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.
Chen, Zhengqin.

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows. - Ann Arbor : ProQuest Dissertations & Theses, 2017 - 178 p.

Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.

Thesis (Ph.D.)--Clarkson University, 2017.

This thesis examines solutions to elliptic partial differential equations (PDEs) from balanced atmospheric flows. We first present a fast numerical solver, implementing the multigrid method. The main theme of this thesis, however, is on the analytical study associated with the elliptic PDEs. In particular, we thoroughly survey the use of the Fokas unified transform method (UTM) in our analytical study, which consists of two directions: (i) obtaining novel analytical solutions to boundary value problems, and (ii) discovering the fundamental transforms associated with a class of boundary value problems. For the first (solution-wise) direction, we review the UTM in depth, solve some example problems, and explore towards solving equations with variable coefficients. For the second (transform-wise) direction, we establish a systematic approach to discover relevant discrete or continuous transforms (including classical Fourier series and Fourier transform), which bypasses the need to resort to completeness relations as required in classical methods. We further show how to explore the relations between discrete and continuous transforms from both spectral and physical senses, using the UTM.

ISBN: 9780355241259Subjects--Topical Terms:

377601
Applied mathematics.

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.
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502 $a Thesis (Ph.D.)--Clarkson University, 2017.
520 $a This thesis examines solutions to elliptic partial differential equations (PDEs) from balanced atmospheric flows. We first present a fast numerical solver, implementing the multigrid method. The main theme of this thesis, however, is on the analytical study associated with the elliptic PDEs. In particular, we thoroughly survey the use of the Fokas unified transform method (UTM) in our analytical study, which consists of two directions: (i) obtaining novel analytical solutions to boundary value problems, and (ii) discovering the fundamental transforms associated with a class of boundary value problems. For the first (solution-wise) direction, we review the UTM in depth, solve some example problems, and explore towards solving equations with variable coefficients. For the second (transform-wise) direction, we establish a systematic approach to discover relevant discrete or continuous transforms (including classical Fourier series and Fourier transform), which bypasses the need to resort to completeness relations as required in classical methods. We further show how to explore the relations between discrete and continuous transforms from both spectral and physical senses, using the UTM.
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