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

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

Journal

Mathematics
, E-ISSN: 2227-7390

Output data

Year: 2025, Volume: 13, Number: 18, Article number : 2979, Pages count : 33 DOI: 10.3390/math13182979

Tags

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

Authors

Bakanov Galitdin ¹ , Chandragiri Sreelatha ² , Kabanikhin Sergey ^2,3 , Shishlenin Maxim ^2,3

Affiliations

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

Funding (1)

Министерство науки и высшего образования РФ
Mathematical Center in Akademgorodok

075-15-2019-1613, 075-15-2022-281

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.

Bakanov G. , Chandragiri S. , Kabanikhin S. , Shishlenin M.
Comparative Analysis of Numerical Methods for Solving 3D Continuation Problem for Wave Equation
Mathematics. 2025. V.13. N18. 2979 :1-33. DOI: 10.3390/math13182979 OpenAlex

Submitted:	Jul 1, 2025
Accepted:	Sep 10, 2025
Published print:	Sep 15, 2025
Published online:	Sep 15, 2025

OpenAlex:

W4414206775

Пока нет цитирований