The paper addresses a numerical solution of a plane–radial boundary inverse problem for the relaxation filtration equation describing fluid flow in an elastically deformable porous medium. The study is motivated by the widespread occurrence of relaxation filtration in hydrogeology, oil and gas production, and subsurface hydromechanics, where reliable identification of medium parameters and reconstruction of unknown boundary actions are essential. Such boundary inverse problems are ill-posed: small perturbations in the input data may cause large deviations in the recovered solution, which makes stable and accurate numerical techniques crucial. The inverse problem is solved using De Souza’s marching method; however, computational experiments show that its accuracy strongly depends on the distance between the measurement point providing the “initial data” and the target boundary. As this distance increases, the error grows due to error accumulation and the intrinsic instability of boundary reconstruction. To improve stability and reduce errors, smoothing splines are employed. The spline approximation effectively suppresses high-frequency noise and stabilizes the recovery of boundary values. As a result, more stable numerical solutions with acceptable accuracy are obtained even under substantial data errors, demonstrating the promise of combining marching methods with smoothing procedures for ill-posed boundary inverse problems of relaxation filtration.
| Mualliflar | Kholiyarov, E.Ch., Turaev, D.Sh., Холияров, Э.Ч., Тураев, Д.Ш. |
|---|---|
| Jurnal | Ҳисоблаш ва амалий математика муаммолари |
| Nashr sanasi | 2026-01-11 |
| Son | 6 |
| Betlar | 112-123 |
| Til | Rus |
| DOI | 10.71310/pcam.6_70.2025.09 |
DOI: 10.71310/pcam.6_70.2025.09 · Maqolaning asl sahifasi
boundary value inverse problem, approximation, regularization, solution stability, smoothing splines, граничная обратная задача, аппроксимация, регуляризация, устойчивость решения, сглаживающие сплайны
Hypersingular integral equations are encountered in a number of fields, such as the dynamics of air and fluid flow, elasticity, and wave propagation theory. Analytical solutions for these integral equations exist, but…
For the first time, a fractal solar collector operating in the cogeneration mode is proposed. In this context, we are talking about a modern innovative system that uses fractal structures to optimize the processes of…
Integrals of rapidly oscillating functions arise mainly in the theory of special functions and Fourier analysis, but also in other applied and computational sciences and engineering, for example, in theoretical physics…
This paper proposes a Context-adaptive Audio-Visual Neural Network (CAVN) model for anomaly detection in public safety systems. Existing approaches primarily rely on visual data and employ simple fusion strategies for…
For the numerical solution of the Dirichlet problem for the Poisson equation, both direct and iterative methods have been developed. However, the required number of arithmetic operations for direct methods, as well as…
In this paper, the Cauchy problem with boundary conditions for an inhomogeneous parabolic equation with changing time direction is investigated. To construct the solution, the method of separation of variables (Fourier…
This study addresses the mathematical modeling of the dispersion process of harmful substances released into the atmosphere in complex urban environments. A mathematical model has been developed to determine the…
The paper models the spatiotemporal dynamics of the Kattakurgan Reservoir area using satellite-based water and vegetation indices combined with ensemble machinelearning methods. Multi-year time series of NDWI, NDVI, and…
This article examines unsteady flows of rheologically complex fluids in a flat channel using the Oldroyd-B model after the actuator is switched off. It is assumed that until the actuator is switched off, the fluid flow…
This article proposes a dynamic model of a coupled thermoelasticity problem under stress. A coupled boundary value problem is formulated, consisting of three differen tial equations for the stress and temperature tensor…