Numerical stability analysis of nonlinear differential equations in engineering systems
Sandip Kulkarnisandip.kulkarni@vupune.ac.inDepartment of Mechanical Engineering Vishwakarma UniversityPune, Maharashtra, 411048, IndiaView full profile → , Urmila Kadamurmila.kadam@dypic.inDr. D Y Patil School of MCA Lohegaon Dr. D Y Patil School of MCAPune, Maharashtra, 412105, IndiaView full profile → , *Deepak Kumar PaswanCorresponding authordeepakkumar0268@gmail.comDepartment of Mechanical Engineering Tulsiramji Gaikwad Patil College of Engineering and TechnologyNagpur, Maharashtra, 441108, IndiaView full profile → , Kumari Shiprakumari.shipra@niu.edu.inSchool of Engineering & Technology Noida International UniversityDepartment of School of Engineering & Technology Noida International UniversityGreater Noida, Uttar Pradesh, 203201, IndiaView full profile → , Bhavana Chandramani Julmebhavanachan@gmail.comDepartment of Computer Science & Engineering Pune Vidyarthi Griha College of Engineering and Technology & G. K. Patel (Wani) Institute of ManagementPune, Maharashtra, 09, IndiaView full profile → , Satyawan L. Dhondgesatyawandhondge@gmail.comDepartment of Mathematics CSMSS Chh. Shahu College of EngineeringChhatrapati Sambhajinagar, Maharashtra, 431001, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 10 Dec 2024
- Published Online:
- 30 Sep 2025
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2367
- Pages:
- 2255–2261
Abstract
Keywords
Subject Classifications
References
[1] G. Y. Kulikov and M. V. Kulikova, “Advanced numerical integration based on Runge–Kutta formulas,” in State Estimation for Nonlinear Continuous–Discrete Stochastic Systems: Numerical Aspects and Implementation Issues, G. Y. Kulikov and M. V. Kulikova, Eds. Cham: Springer International Publishing, pp. 111–225 (2024).
[2] S. H. Nasab, C. A. Pereira, and B. C. Vermeire, “Optimal Runge–Kutta stability polynomials for multidimensional high-order methods,” J. Sci. Comput., vol. 89, no. 1, pp. 11 (2021).
[3] W. Ding, Y. Li, and M. Wei, “Jacobi method for dual quaternion Hermitian eigenvalue problems and applications,” J. Appl. Math. Comput., vol. 70, no. 4, pp. 3749–3766 (2024).
[4] F. Ihssen, F. R. Sattler, and N. Wink, “Numerical RG-time integration of the effective potential: Analysis and benchmark,” Phys. Rev. D, vol. 107, no. 11, pp. 114009 (Jun. 2023).
[5] A. Mihara, M. Zaks, E. E. N. Macau, and R. O. Medrano-T, “Basin sizes depend on stable eigenvalues in the Kuramoto model,” Phys. Rev. E, vol. 105, no. 5, pp. L052202 (May 2022).
[6] W.H. Tang, W.W. Li, J.H. Zheng, C.Q. Wu, L.X. Wang, Q.L. Wei, Q.H. Wu, “A composite voltage stability index for integrated energy systems based on L-index and the minimum eigenvalue of reduced Jacobian matrix,” Int. J. Electr. Power Energy Syst., vol. 141, pp. 108136 (2022).
[7] S. Kothawade and I. Zellar, “Blockchain-enabled transformation in public administrative services: A comparative analysis of current applications and future potential,” Int. J. Recent Adv. Eng. Technol. (IJRAET), vol. 14, no. 1, pp. 127–128 (Apr. 2025).
[8] R. H. Hilal, N. A. M. Al-Karamy, and S. M. Aljassas, “Derivation of a numerical method for calculating single integrals,” J. Interdiscip. Math., vol. 28, no. 1, pp. 327–338 (2025).
[9] L. Bouzid, N. Lahmar-Ablaoui, and M. H. Maamar, “New 2D numerical integration formula based on the Legendre wavelets,” J. Interdiscip. Math., vol. 26, no. 5, pp. 835–847 (2023).
[10] V. Deshpande, D. Khubalkar, A. Dhablia, M. J. Pasha, D. Dhabliya, and Y. Gandhi, “Enhancing financial transaction security with lightweight cryptographic algorithms,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-B, pp. 741–751 (2024).
[11] D. Goyal, A. Kumar, Y. Gandhi, and V. Khetani, “Securing wireless sensor networks with novel hybrid lightweight cryptographic protocols,” Journal of Discrete Mathematical Sciences and Cryptography, vol. 27, no. 2-B, pp. 703–714 (2024).
