Premium
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.