On the definition of surface potentials for finite-difference operators
The author introduces a concept of single- and double-layer potentials for linear constant-coefficient finite difference operators of second order on rectangular mesh in 2-D. Although similar to the conventional potentials for differential operators, the discrete potentials are introduced and studied completely independently. The resulting discrete ``surface'' potentials appear to be solutions to systems of linear difference equations with special source terms. The possible application of such new mathematical objects is active shielding and control of sound of domain of interest.
scientific article; zbMATH DE number 1968060