Kyungpook Mathematical Journal

Department of Mathematics, Kyungpook National University (경북대학교 자연과학대학 수학과)
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A New Approach for the Derivation of a Discrete Approximation Formula on Uniform Grid for Harmonic Functions

  • Kim, Philsu (Department of Mathematics, Kyungpook National University) ;
  • Choi, Hyun Jung (Department of Mathematics, Kyungpook National University) ;
  • Ahn, Soyoung (Department of Mathematics, Kyungpook National University)
  • Received : 2007.05.21
  • Published : 2007.12.23
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Abstract

The purpose of this article is to find a relation between the finite difference method and the boundary element method, and propose a new approach deriving a discrete approximation formula as like that of the finite difference method for harmonic functions. We develop a discrete approximation formula on a uniform grid based on the boundary integral formulations. We consider three different boundary integral formulations and derive one discrete approximation formula on the uniform grid for the harmonic function. We show that the proposed discrete approximation formula has the same computational molecules with that of the finite difference formula for the Laplace operator ${\nabla}^2$.

Keywords

References

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