Atlas home || Conferences | Abstracts | about Atlas

International Conference on Mathematical Modeling and Scientific Computing
April 2-6, 2001
Middle East Technical University and Selcuk University
Ankara and Konya, Turkey

Organizers
F. Bornemann (Munich University of Tecnology, Germany), H. Bulgak (Selcuk University, Konya, Turkey), V. Ganzha (Munich University of Technology, Germany), B. Karasozen (METU, Ankara, Turkey), A. Sinan (Selcuk University, Konya, Turkey), C. Zenger (Munich University of Technology, Germany)

View Abstracts
Conference Homepage

The Block-Grid Method for Solving Laplace's Equation on Polygons with analytic mixed boundary conditions
by
Mehmet Bozer
Department of Mathematics, Eastern Mediterranean University, Northern Cyprus
Coauthors: A.A. Dosiyev(Department of Mathematics, Eastern Mediterranean University, Northern Cyprus)

The Block-Grid method (BGM) is one of high accurate combined method (an approximation of the special integral representation of the exact solution around the vertices, i.e., on block-sectors and a finite difference approximation of Laplace's equation outside the block sectors) for solving the Laplace equation on polygons with corner and boundary singularities, when boundary conditions given by algebraic polynomials, was proposed and justified in [1], [2]. In this paper we present and justify BGM for solving the Laplace equation under analytic mixed boundary conditions. In this case a covering of the polygon by finite number of overlapping block sectors and rectangles depends not only with the geometry of the domain also on the functions appearing in the boundary conditions.

[1] A.A. Dosiyev, A Block-Grid method for increasing accuracy in the solution of the Laplace equation on polygons. Russian Acad. Sci. Dokl. Math.Vol.45, No.2 (1992), 396-399.

[2] A.A. Dosiyev, A Block-Grid method for increased accuracy for solving Drichlet's problem for Laplace's equation on polygons.Comp. Maths Math. Phys., Vol.34, No.5 (1994), 591-604.

Date received: March 6, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cagk-86.