I. E. Stepanova, I. I. Kolotov, A. G. Yagola, A. N. Levashov, “On the uniqueness of determining the mesh fundamental solution of Laplace’s equation in the theory of discrete potential”, Zh. Vychisl. Mat. Mat. Fiz., 2024, Volume 64, Number 7,Pages <nobr>1253

This article is cited in 3 papers

Partial Differential Equations

On the uniqueness of determining the mesh fundamental solution of Laplace’s equation in the theory of discrete potential

I. E. Stepanova^a, I. I. Kolotov^b, A. G. Yagola^b, A. N. Levashov^b

^a Schmidt Institute of Physics of the Earth, Russian Academy of Sciences, 123242, Moscow, Russia
^b Lomonosov Moscow State University, 119992, Moscow, Russia

Abstract: The paper examines the problem of unique determination of the fundamental solution of a mesh analogue of Laplace’s equation within the theory of discrete gravitational potential. The mesh fundamental solution of the finite-difference analogue of Laplace’s equation plays a key role in reconstructing a continuously distributed source of gravitational or magnetic field from heterogeneous and different-precision data obtained at points of a certain mesh set.

Key words: unique determination, fundamental solution, discrete gravitational potential.

UDC: 550.83+550.81

Received: 13.03.2024

DOI: 10.31857/S0044466924070108