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Potentially theoretical schemes in the fundamental solutionsmethod 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 onecan be obtained

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