A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in Ck,λ
Joint Authors
Dosiyev, A. A.
Cival Buranay, S.
Source
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-11, 11 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-06-20
Country of Publication
Egypt
No. of Pages
11
Main Subjects
Abstract EN
The integral representations of the solution around the vertices of the interior reentered angles (on the “singular” parts) are approximated by the composite midpoint rule when the boundary functions are from C4,λ, 0<λ<1.
These approximations are connected with the 9-point approximation of Laplace's equation on each rectangular grid on the “nonsingular” part of the polygon by the fourth-order gluing operator.
It is proved that the uniform error is of order O(h4+ε), where ε>0 and h is the mesh step.
For the p-order derivatives (p=0,1,…) of the difference between the approximate and the exact solutions, in each “ singular” part O((h4+ε)rj1/αj-p) order is obtained; here rj is the distance from the current point to the vertex in question and αjπ is the value of the interior angle of the jth vertex.
Numerical results are given in the last section to support the theoretical results.
American Psychological Association (APA)
Dosiyev, A. A.& Cival Buranay, S.. 2013. A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in Ck,λ. Abstract and Applied Analysis،Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-504522
Modern Language Association (MLA)
Dosiyev, A. A.& Cival Buranay, S.. A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in Ck,λ. Abstract and Applied Analysis No. 2013 (2013), pp.1-11.
https://search.emarefa.net/detail/BIM-504522
American Medical Association (AMA)
Dosiyev, A. A.& Cival Buranay, S.. A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in Ck,λ. Abstract and Applied Analysis. 2013. Vol. 2013, no. 2013, pp.1-11.
https://search.emarefa.net/detail/BIM-504522
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-504522