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Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations

Author

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  • Hongyu Qin
  • Zhiyong Wang
  • Fumin Zhu
  • Jinming Wen

Abstract

This paper is concerned with stability analysis of additive Runge-Kutta methods for delay-integro-differential equations. We show that if the additive Runge-Kutta methods are algebraically stable, the perturbations of the numerical solutions are controlled by the initial perturbations from the system and the methods.

Suggested Citation

  • Hongyu Qin & Zhiyong Wang & Fumin Zhu & Jinming Wen, 2018. "Stability Analysis of Additive Runge-Kutta Methods for Delay-Integro-Differential Equations," International Journal of Differential Equations, Hindawi, vol. 2018, pages 1-5, June.
    • Handle: RePEc:hin:jnijde:8241784
    DOI: 10.1155/2018/8241784
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    Cited by:

    1. Zhang, Chunmei & Han, Bang-Sheng, 2020. "Stability analysis of stochastic delayed complex networks with multi-weights based on Razumikhin technique and graph theory," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).
    2. Tan, Jianguo & Tan, Yahua & Guo, Yongfeng & Feng, Jianfeng, 2020. "Almost sure exponential stability of numerical solutions for stochastic delay Hopfield neural networks with jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    3. Liu, Zhiguang & Zhu, Quanxin, 2023. "Ultimate boundedness of impulsive stochastic delay differential equations with delayed impulses," Statistics & Probability Letters, Elsevier, vol. 199(C).
    4. Rajasekar, S.P. & Pitchaimani, M. & Zhu, Quanxin, 2020. "Progressive dynamics of a stochastic epidemic model with logistic growth and saturated treatment," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 538(C).

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