Email this article A Study of Numerical Methods for Solving the Nonlinear Energy Resources Supply-Demand System
- Authors: Vo V.T.1, Noeiaghdam S.2, Dreglea A.I.1, Sidorov D.N.1
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Affiliations:
- Irkutsk National Research Technical University
- Irkutsk National Research Technical University, Institute of Mathematics, Henan Academy of Sciences
- Issue: Vol 27, No 2 (2025)
- Pages: 143-170
- Section: Mathematics
- Submitted: 10.10.2025
- Accepted: 10.10.2025
- Published: 28.05.2025
- URL: https://journal-vniispk.ru/2079-6900/article/view/324412
- ID: 324412
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Abstract
n 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.
About the authors
Van T. Vo
Irkutsk National Research Technical University
Email: votruong.90@gmail.com
ORCID iD: 0009-0008-2701-4775
PhD Student, Irkutsk National Research Technical University
Russian Federation, 83, Lermontov St., Irkutsk 664074, RussiaSamad Noeiaghdam
Irkutsk National Research Technical University, Institute of Mathematics, Henan Academy of Sciences
Email: snoei@hnas.ac.cn
ORCID iD: 0000-0002-2307-0891
Ph.D. (Phys. and Math.), Professor, Institute of Mathematics, Henan Academy of Sciences
ChinaAliona I. Dreglea
Irkutsk National Research Technical University
Email: adreglea@gmail.com
ORCID iD: 0000-0002-5032-0665
Ph.D. (Phys. and Math.), Associate Professor, Senior Researcher, Scientific Research Department
Russian Federation, 83 Lermontov St., Irkutsk 664074, RussiaDenis N. Sidorov
Irkutsk National Research Technical University
Author for correspondence.
Email: dsidorov@isem.irk.ru
ORCID iD: 0000-0002-3131-1325
D. Sc. (Phys. and Math.), Professor, Chief Researcher, Applied Mathematics Department
Russian Federation, 83, Lermontov St., Irkutsk 664074, RussiaReferences
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