Vestnik КRAUNC. Fiz.-Mat. Nauki. 2025. vol. 50. no. 1. P. 169 – 183. ISSN 2079-6641

INFORMATION AND COMPUTING TECHNOLOGIES
https://doi.org/10.26117/2079-6641-2025-50-1-169-183
Research Article
Full text in Russian
MSC  86-08

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Investigation of the Effectiveness of Numerical Methods for Solving a Mathematical Model of High-Frequency Geoacoustic Emission

D. F. Sergienko¹²^{\ast}, R. I. Parovik²

¹Vitus Bering Kamchatka State University, 683032, Petropavlovsk-Kamchatsky, Pogranichnaya str., 4, Russia
²Institute of Cosmophysical Research and Radio Wave Propagation, Far Eastern Branch of the Russian Academy of Sciences, 684034, Paratunka village, Mirnaya str., 7, Russia

Abstract. This paper presents a study of four numerical methods for solving a mathematical model of high-frequency geoacoustic emission: the Rosenbrock method (4th order of accuracy), Radau, BDF, and LSODA. The Rozobrok method is implemented in the Python programming language, the rest of the methods were taken from the Scipy Python library. The paper describes each numerical method, which makes it possible to justify the choice of methods for solving the problem. The main purpose of the work is a comparative analysis of their effectiveness according to the criteria of accuracy, stability and computational complexity. The order of accuracy of the methods using the Runge rule is estimated in Python, and their characteristics are analyzed when solving a system of two linear ordinary differential equations of the second order with non-constant coefficients. The paper presents graphs of the dependence of the order of accuracy on the step of calculations, waveforms of solutions and phase trajectories of a mathematical model that clearly demonstrate the behavior of the system under various parameters. Special attention is paid to the adaptability of the methods to the rigidity of the system due to the presence of rapidly attenuating and high-frequency components. The results show that the Rosenbrock method provides high accuracy with an analytically specified Jacobi matrix, while the order of the other methods has an experimental order lower than the theoretical one. The data obtained allows us to determine the optimal modeling method depending on the required accuracy and computing resources. The study contributes to the development of numerical approaches to the analysis of geoacoustic processes and can be used in predicting deformation phenomena in rocks.

Key words: geoacoustic emission, model, waveforms, phase trajectory, Rosenbrock method, BDF, Radau, LSODA, python.

Received: 05.04.2025; Revised: 16.04.2025; Accepted: 17.04.2025; First online: 18.04.2025

For citation. Sergienko D. F., Parovik R. I. Investigation of the Effectiveness of Numerical Methods for Solving a Mathematical Model of High-Frequency Geoacoustic Emission. Vestnik KRAUNC. Fiz.-mat. nauki. 2025, 50: 1, 169-183. EDN: PHPEAX. https://doi.org/10.26117/2079-6641-2025-50-1-169-183.

Funding. The work was carried out within the framework of the state assignment of IKIR FEB RAS No. 124012300245-2.

Competing interests. There are no conflicts of interest regarding authorship and publication.

Contribution and Responsibility. All authors contributed to this article. Authors are solely responsible for providing the final version of the article in print. The final version of the manuscript was approved by all authors.

^{\ast}Correspondence: E-mail: darya@ikir.ru

The content is published under the terms of the Creative Commons Attribution 4.0 International License

© Sergienko D. F., Parovik R. I., 2025

© Institute of Cosmophysical Research and Radio Wave Propagation, 2025 (original layout, design, compilation)

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Information about the authors

Sergienko Daria Faritovna – aspirant of the Department of Mathematics and Computer Science, Vitus Bering Kamchatka State University, Petropavlovsk-Kamchatsky, Russia; programmer of the Laboratory of Acoustic Research, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, S. Paratunka, Russia ORCID 0009-0008-6512-4537.

Parovik Roman Ivanovich – DSc (Phys. & Math.), Associate Professor, Professor of the Far Eastern Branch of the Russian Academy of Sciences, Academician of the Russian Academy of Sciences, Leading Researcher at the Laboratory of Modeling Physical Processes, Institute of Cosmophysical Research and Radio Wave Propagation FEB RAS, S. Paratunka, Russia ORCID 0000-0002-1576-1860.

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