Boundary Contraction Solution of Laplace's Differential Equation

  • Authors:

  • Harold W. Milnes;Renfrey B. Potts

  • Affiliations:

  • General Motors Corporation, Detroit, Michigan;General Motors Corporation, Detroit, Michigan

  • Venue:
  • Journal of the ACM (JACM)
  • Year:
  • 1959

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Abstract

A numerical method is introduced for solution of the Dirichlet problem within a circle. The data prescribed on the original boundary is used to compute the solution at mesh points on a concentric circle of slightly smaller radius, thereby defining another boundary value problem over the smaller circle. The solution for the entire region is obtained by successive contractions of the boundary in this way. Appropriate approximating relations are presented and their stability is discussed.