On the Uniqueness of the Finite-Difference Analogues of the Fundamental Solution of the Heat Equation and the Wave Equation in Discrete Potential Theory
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 differenti...
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| Veröffentlicht in: | Computational mathematics and mathematical physics 2024, Vol.64 (12), p.2893-2904 |
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| container_issue | 12 |
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| container_title | Computational mathematics and mathematical physics |
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| creator | Stepanova, I. E. Kolotov, I. I. Shchepetilov, A. V. Yagola, A. G. Levashov, A. N. |
| description | 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. |
| doi_str_mv | 10.1134/S0965542524701707 |
| format | Article |
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| source | Springer Nature - Complete Springer Journals |
| subjects | Computational Mathematics and Numerical Analysis Finite difference method Heat sources Inverse problems Mathematical analysis Mathematics Mathematics and Statistics Partial Differential Equations Potential theory Thermodynamics Wave equations |
| title | On the Uniqueness of the Finite-Difference Analogues of the Fundamental Solution of the Heat Equation and the Wave Equation in Discrete Potential Theory |
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