國立虎尾科技大學 |

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.

紀錄類型:	書目-語言資料,手稿 : Monograph/item
正題名/作者:	Solutions of Quasilinear PDEs in Balanced Atmospheric Flows./
作者:	Chen, Zhengqin.
面頁冊數:	1 online resource (178 pages)
附註:	Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
Contained By:	Dissertation Abstracts International79-02B(E).
標題:	Applied mathematics. -
電子資源:	click for full text (PQDT)
ISBN:	9780355241259

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

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows. - 1 online resource (178 pages)

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

Thesis (Ph.D.)

Includes bibliographical references

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.

Electronic reproduction.
Ann Arbor, Mich. :
ProQuest,
2018

Mode of access: World Wide Web

ISBN: 9780355241259Subjects--Topical Terms:

1069907
Applied mathematics.
Index Terms--Genre/Form:

554714
Electronic books.

Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.
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245 1 0 $a Solutions of Quasilinear PDEs in Balanced Atmospheric Flows.
264 0 $c 2017
300 $a 1 online resource (178 pages)
336 $a text $b txt $2 rdacontent
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500 $a Source: Dissertation Abstracts International, Volume: 79-02(E), Section: B.
500 $a Adviser: Scott R. Fulton.
502 $a Thesis (Ph.D.) $c Clarkson University $d 2017.
504 $a Includes bibliographical references
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.
533 $a Electronic reproduction. $b Ann Arbor, Mich. : $c ProQuest, $d 2018
538 $a Mode of access: World Wide Web
650 4 $a Applied mathematics. $3 1069907
655 7 $a Electronic books. $2 local $3 554714
690 $a 0364
710 2 $a ProQuest Information and Learning Co. $3 1178819
710 2 $a Clarkson University. $b Mathematics. $3 1182492
773 0 $t Dissertation Abstracts International $g 79-02B(E).
856 4 0 $u http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10605390 $z click for full text (PQDT)