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

Abstract

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.

Keywords

• Extremal weighted polynomial
• weak convergence
• normalized counting measure on zeros
• fundamental solutions method
• Dirichlet problems
• charge points.