Mathematical Methods in the Applied Sciences · 2002 · 35 citations · 8 references
Numerical AnalysisMethod Of Fundamental SolutionEngineeringGeneralized FunctionRiemann-hilbert ProblemPotential TheoryFinite Difference PotentialsAnalytic Number TheoryDiscrete Function TheoryDifference PotentialsPotential Theoretical MethodUniform LatticeDiscrete MathematicsFunctional AnalysisDiscrete Integrable System
Abstract 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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