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Alternating direction implicit finit...

Wray, Steven.

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Alternating direction implicit finite difference methods for the heat equation on general domains in two and three dimensions.

紀錄類型:	書目-電子資源 : Monograph/item
正題名/作者:	Alternating direction implicit finite difference methods for the heat equation on general domains in two and three dimensions./
作者:	Wray, Steven.
出版者:	Ann Arbor : ProQuest Dissertations & Theses, : 2016,
面頁冊數:	111 p.
附註:	Source: Masters Abstracts International, Volume: 55-05.
Contained By:	Masters Abstracts International55-05(E).
標題:	Applied mathematics. -
電子資源:	http://pqdd.sinica.edu.tw/twdaoapp/servlet/advanced?query=10129292
ISBN:	9781339871837

Alternating direction implicit finite difference methods for the heat equation on general domains in two and three dimensions.
Wray, Steven.

Alternating direction implicit finite difference methods for the heat equation on general domains in two and three dimensions. - Ann Arbor : ProQuest Dissertations & Theses, 2016 - 111 p.

Source: Masters Abstracts International, Volume: 55-05.

Thesis (M.S.)--Colorado School of Mines, 2016.

Alternating direction implicit methods are a class of finite difference methods for solving parabolic PDEs in two and three dimensions. The convergence properties of these methods on rectangular domains are well-understood. We wish to extend this approach to solve the heat equation on arbitrary domains. We begin by dropping a perturbation term for the boundary conditions of the Peaceman-Rachford method in the Dirichlet problem on a two-dimensional box. We show theoretically that this modified method converges with order two under the discrete maximum norm. This is confirmed by numerical tests that show the modified method converges with order two under both the discrete maximum norm and the discrete L2 norm. In three dimensions, similar modifications allow us to extend the Douglas method. On an arbitrary domain, the extended method converges with order two under the discrete L2 norm but with order one under the discrete maximum norm.

ISBN: 9781339871837Subjects--Topical Terms:

2122814
Applied mathematics.

Alternating direction implicit finite difference methods for the heat equation on general domains in two and three dimensions.
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300 $a 111 p.
500 $a Source: Masters Abstracts International, Volume: 55-05.
500 $a Includes supplementary digital materials.
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520 $a Alternating direction implicit methods are a class of finite difference methods for solving parabolic PDEs in two and three dimensions. The convergence properties of these methods on rectangular domains are well-understood. We wish to extend this approach to solve the heat equation on arbitrary domains. We begin by dropping a perturbation term for the boundary conditions of the Peaceman-Rachford method in the Dirichlet problem on a two-dimensional box. We show theoretically that this modified method converges with order two under the discrete maximum norm. This is confirmed by numerical tests that show the modified method converges with order two under both the discrete maximum norm and the discrete L2 norm. In three dimensions, similar modifications allow us to extend the Douglas method. On an arbitrary domain, the extended method converges with order two under the discrete L2 norm but with order one under the discrete maximum norm.
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