On finite difference potentials and their applications in a discrete function theory | Zendy

Gürlebeck K. | Zendy; Hommel A. | Zendy

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On finite difference potentials and their applications in a discrete function theory

Author(s) -

Gürlebeck K.,

Hommel A.

Publication year - 2002

Publication title -

mathematical methods in the applied sciences

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.719

H-Index - 65

eISSN - 1099-1476

pISSN - 0170-4214

DOI - 10.1002/mma.389

Subject(s) - mathematics , cauchy distribution , laplace transform , boundary value problem , finite difference , mathematical analysis , discrete poisson equation , operator (biology) , cauchy's integral formula , laplace's equation , lattice (music) , finite difference method , cauchy problem , initial value problem , biochemistry , chemistry , physics , repressor , transcription factor , acoustics , gene

We present a potential theoretical method which is based on the approximation of the boundary value problem by a finite difference problem on a uniform lattice. At first the discrete fundamental solution of the Laplace equation is studied and the theory of difference potentials is described. In the second part we define a discrete Cauchy integral operator and a Teodorescu transform. In addition a Borel–Pompeiu formula can be formulated. Copyright © 2002 John Wiley & Sons, Ltd.

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