V. T. Vo¹, S. Noeiaghdam^{1, 2}, A. I. Dreglea¹, D. N. Sidorov¹

¹Irkutsk National Research Technical University (Irkutsk, Russia)

²Institute of Mathematics, Henan Academy of Sciences (Zhengzhou, China)

Abstract. In this study, we implement and estimate various numerical methods for solving a nonlinear differential equation system modeling energy resources supply-demand dynamics. Both single-step methods (Taylor series, Runge-Kutta) and multi-step methods (Adams – Bashforth, Adams Predictor-Corrector) are employed. In addition to standard fourth-order methods, higher-order techniques such as the fifth-order Runge-Kutta method and the sixth- order Taylor series method are also applied. Furthermore, along with fixed-step numerical methods, we implement and assess adaptive step-size methods, including the explicit Runge- Kutta method of order 5(4) (that is RK45), the explicit Runge-Kutta method of order 8(5,3) (or DOP853), the implicit Runge-Kutta method from the Radau IIA family of order 5 (Radau), the implicit method based on backward differentiation formulas (BDF), and the Adams/BDF method with automatic switching (LSODA). The results indicate that, in the cases we considered, single-step methods are more effective than multi-step ones in capturing and tracking rapid variations of the system, while multi-step methods require less computation time. Adaptive step-size numerical methods demonstrate both flexibility and stability. Through the evaluation and analysis of numerical solutions obtained by various methods, the behaviour and dynamic characteristics of the system are explored.

Key Words: energy supply and demand system, Runge-Kutta method, Taylor series, Adams-Bashforth method, Adams Predictor-Corrector method, RK45, DOP853, Radau, BDF, LSODA

For citation: V. T. Vo, S. Noeiaghdam, A. I. Dreglea, D. N. Sidorov. A Study of Numerical Methods for Solving the Nonlinear Energy Resources Supply-Demand System. Zhurnal Srednevolzhskogo matematicheskogo obshchestva. 27:2(2025), 143–170. DOI: https://doi.org/10.15507/2079-6900.27.202502.143-170

Information about the authors:

Van T. Vo, PhD Student, Irkutsk National Research Technical University (83, Lermontov St., Irkutsk 664074, Russia), ORCID: https://orcid.org/0009-0008-2701-4775, votruong.90@gmail.com

Samad Noeiaghdam, Ph.D. (Phys. and Math.), Professor, Institute of Mathematics, Henan Academy of Sciences (Zhengzhou, 450046, China), ORCID: https://orcid.org/0000- 0002-2307-0891, snoei@hnas.ac.cn

Aliona I. Dreglea, Ph.D. (Phys. and Math.), Associate Professor, Senior Researcher, Scientific Research Department, Irkutsk National Research Technical University (83 Lermontov St., Irkutsk 664074, Russia), ORCID: https://orcid.org/0000-0002-5032-0665, adreglea@gmail.com

Denis N. Sidorov, D. Sc. (Phys. and Math.), Professor, Chief Researcher, Applied Mathematics Department, Melentiev Energy Systems Institute Siberian Branch of Russian Academy of Science (130 Lermontov St., Irkutsk 664033, Russia); ORCID: https://orcid.org/0000-0002-3131-1325, dsidorov@isem.irk.ru