On the uniqueness of the finite-difference analogues of the fundamental solution of the heat equation and the wave equation in discrete potential theory
Abstract:
The paper considers the problem of uniquely determining the fundamental solution of the finite-difference analogs of the wave equation and the heat equation in the framework of the discrete potential theory. Finite-difference fundamental solutions of finite-difference analogues of partial differential equations make it possible to solve direct and inverse problems of reconstructing wave and heat sources in various media from heterogeneous and multi-current information about the corresponding physical fields. The article considers formulations with Dirichlet conditions in three- and four-dimensional Cartesian spaces.
Key words:uniqueness, fundamental solution, discrete heat potential, discrete wave potential.
