A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in
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 These approximations are connected with the 9-point approximation of Laplace's equati...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2013/864865 |
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| author | A. A. Dosiyev S. Cival Buranay |
| author_facet | A. A. Dosiyev S. Cival Buranay |
| author_sort | A. A. Dosiyev |
| collection | DOAJ |
| description | 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 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 where and is the mesh step. For the -order derivatives () of the difference between the approximate and the exact solutions, in each “ singular” part order is obtained; here is the distance from the current point to the vertex in question and is the value of the interior angle of the th vertex. Numerical results are given in the last section to support the theoretical results. |
| format | Article |
| id | doaj-art-51b37a86685b4db9bfd6d73b43f6ffe2 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-51b37a86685b4db9bfd6d73b43f6ffe22025-08-20T03:36:38ZengWileyAbstract and Applied Analysis1085-33751687-04092013-01-01201310.1155/2013/864865864865A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions inA. A. Dosiyev0S. Cival Buranay1Department of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, Mersin 10, TurkeyDepartment of Mathematics, Eastern Mediterranean University, Gazimagusa, North Cyprus, Mersin 10, TurkeyThe 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 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 where and is the mesh step. For the -order derivatives () of the difference between the approximate and the exact solutions, in each “ singular” part order is obtained; here is the distance from the current point to the vertex in question and is the value of the interior angle of the th vertex. Numerical results are given in the last section to support the theoretical results.http://dx.doi.org/10.1155/2013/864865 |
| spellingShingle | A. A. Dosiyev S. Cival Buranay A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in Abstract and Applied Analysis |
| title | A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in |
| title_full | A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in |
| title_fullStr | A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in |
| title_full_unstemmed | A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in |
| title_short | A Fourth-Order Block-Grid Method for Solving Laplace's Equation on a Staircase Polygon with Boundary Functions in |
| title_sort | fourth order block grid method for solving laplace s equation on a staircase polygon with boundary functions in |
| url | http://dx.doi.org/10.1155/2013/864865 |
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