Comparative Analysis of Numerical Methods for Solving 3D Continuation Problem for Wave Equation

Bakanov G. Chandragiri S. Kabanikhin S. Shishlenin M.
September 2025 Multidisciplinary Digital Publishing Institute (MDPI)

Mathematics
2025 #13 Issue 18

In this paper, we develop the explicit finite difference method (FDM) to solve an ill-posed Cauchy problem for the 3D acoustic wave equation in a time domain with the data on a part of the boundary given (continuation problem) in a cube. FDM is one of the numerical methods used to compute the solutions of hyperbolic partial differential equations (PDEs) by discretizing the given domain into a finite number of regions and a consequent reduction in given PDEs into a system of linear algebraic equations (SLAE). We present a theory, and through Matlab Version: 9.14.0.2286388 (R2023a), we find an efficient solution of a dense system of equations by implementing the numerical solution of this approach using several iterative techniques. We extend the formulation of the Jacobi, Gauss–Seidel, and successive over-relaxation (SOR) iterative methods in solving the linear system for computational efficiency and for the properties of the convergence of the proposed method. Numerical experiments are conducted, and we compare the analytical solution and numerical solution for different time phenomena.

acoustic wave equation , continuation problem , finite difference method , inverse and ill-posed problem , numerical analysis , regularization

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Faculty of Natural Sciences, Khoja Akhmet Yassawi International Kazakh-Turkish University, Turkestan, 161200, Kazakhstan
Sobolev Institute of Mathematics, Novosibirsk, 630090, Russian Federation
Institute of Computational Mathematics and Mathematical Geophysics, Novosibirsk, 630090, Russian Federation

Faculty of Natural Sciences
Sobolev Institute of Mathematics
Institute of Computational Mathematics and Mathematical Geophysics

10 лет помогаем публиковать статьи Международный издатель

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