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International Conference: 2004 - Dynamical Systems and Applications
July 5-10, 2004

Antalya, Turkey

Organizers
Akca Haydar, Basem S. Attili, Boucherif Abdelkader, Cho Yeol Je, Covachev Valery, Gyori Istvan, Maksimov Vyacheslav, Stavroulakis Ioannis P.

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A Difference-Analytical Method for Solving Laplace's Boundary Value Problem with Singularities
by
Suzan Cival Buranay
Eastern Mediterranean University, Gazimagusa, Cyprus, Mersin 10, Turkey
Coauthors: A.A. Dosiyev

A difference -analytical method of solving the mixed boundary value problem for Laplace's equation on polygons (which can have broken sections and be multiply connected) is described and justified. The uniform estimate for the error of the approximate solution is of order O( h2) , where h is the mesh step, for the errors of derivatives of order p, p=1, 2, ..., in a finite neighbourhood of vertices, of order O(h2/rjp-1/\lambdaj) , where rj is the distance from the current point to the vertex in question, \lambdaj=1/\alphaj or \lambdaj=1/(2\alphaj), depending on the types of boundary conditions, \alphaj\pi  is the value of the angle. The last part of the paper is devoted to illustrate numerical experiments.

Date received: March 1, 2004

Copyright © 2004 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 # canu-04.