Stability and Convergence Analysis of Runge-Kutta Methods for a Class of Nonlinear Functional Differential-Algebraic Equations_Vol. 2 No. 5 (JHET 2025)_Journal of Higher Education Teaching (ISSN: 3005-5776)

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Stability and Convergence Analysis of Runge-Kutta Methods for a Class of Nonlinear Functional Differential-Algebraic Equations

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DOI: https://doi.org/10.62517/jhet.202515519

Author(s)

Zhang Peng

Affiliation(s)

School of Mathematics, Qilu Normal University, Jinan, Shandong, China

Abstract

In mathematics teaching, the numerical analysis course has always been one of the most important bridges connecting mathematical theory and scientific practice. It directly affects students' learning effects in mathematics learning and is even more related to students' ability and quality in solving complex engineering problems. In the traditional mathematics teaching process, the focus of education and teaching is mostly placed on the numerical teaching methods of ordinary differential equations. However, insufficient attention has been paid to cutting-edge models and nonlinear functional differential-algebraic equations. Therefore, it is necessary to analyze this content, strengthen the cultivation of theoretical foundations, help students develop critical learning thinking, integrate it into the entire knowledge system, and stimulate students' innovative awareness.

Keywords

A Class of Nonlinear Functional Differential-Algebraic Equations; Runge-Kutta Method; Stability; Convergence

References

[1] Li, J. F., & Bi, H. (2024). Stability Analysis of Implicit-Explicit Runge-Kutta Ultra-Weak Local Discontinuous Galerkin Method for Linear Fourth-Order Equations. Journal of Natural Science of Heilongjiang University, 41(06), 700-710. [2] Zhao, Q., Li, L. J., Wu, Z. C., et al. (2024). Dynamic Research on the Terminal Executor for Camellia Bud Harvesting Based on Runge-Kutta Method. Chinese Journal of Construction Machinery, 22(06), 707-711+716. [3] Xie, Y. W., & Zhang, J. H. (2024). Temporal Parallel Preconditioner for Second-Order Diagonal Runge-Kutta Method for Solving Heat Conduction Equations. Journal of Jinggangshan University (Natural Science Edition), 45(06), 8-16. [4] Ai, D. X. (2024). Stability and Convergence Analysis of Runge-Kutta Methods for a Class of Nonlinear Functional Differential-Algebraic Equations [Master's Thesis]. Xiangtan University. [5] Fan, Z. C. (2024). Input-State Stability of Runge-Kutta Methods for Nonlinear Control Systems. Journal of Minjiang University, 45(02), 1-6.