International Journal of Mathematics and Mathematical Sciences
Volume 22 (1999), Issue 2, Pages 349-365

Mathematical approach and numerical analysis to the fundamental solutions method of Dirichlet problem

Tetsuo Inoue

Department of Information Systems Engineering, Kobe University of Mercantile Marine, Kobe, Japan

Received 31 May 1996; Revised 7 July 1997

Copyright © 1999 Tetsuo Inoue. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Potentially theoretical schemes in the fundamental solutions method will be proposed for Dirichlet problems of unbounded and bounded Jordan domains. The asymptotic theorem on extremal weighted polynomials will play fundamental roles to introduce a new scheme and to determine the distribution of charge points. Typical examples of the method will show that the numerical results of higher accuracy than those of the the conventional one can be obtained.