Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional Equations

Keywords

Runge–Kutta methods, Nonlinear system, Stability (learning theory), Mathematics, Differential equation

References

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• Nonlinear stability of one-leg methods for delay differential equations of neutral typeWansheng Wang, Yuan Zhang, Shoufu Li — 2008
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• Stability results for systems described by coupled retarded functional differential equations and functional difference equationsIasson Karafyllis, Pierdomenico Pepe, Zhong‐Ping Jiang — 2007
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• Numerical Solution of Implicit Neutral Functional Differential EquationsYunkang Liu — 1999
• Nonlinear stability of general linear methods for neutral delay differential equationsWansheng Wang, Shoufu Li, Kai Su — 2009
• Stability analysis of one-leg methods for nonlinear functional differential and functional equationsYuexin Yu, Liping Wen — 2010
• Non-linear stability of a general class of differential equation methodsKevin Burrage, J. C. Butcher — 1980

Cited by

• Computational Techniques Based on Runge-Kutta Method of Various Order and Type for Solving Differential EquationsVijeyata Chauhan, Pankaj Kumar Srivastava — 2019
• Solving nonlinear functional-differential and functional equations with constant delay via block boundary value methodsXiaoqiang Yan, Chengjian Zhang — 2019
• Convergence and stability of extended BBVMs for nonlinear delay-differential-algebraic equations with piecewise continuous argumentsChengjian Zhang, Xiaoqiang Yan — 2020
• Stability and Convergence of the Canonical Euler Splitting Method for Nonlinear Composite Stiff Functional Differential-Algebraic EquationsHongliang Liu, Y. Zhang, Haodong Li — 2022
• Modeling Infectious Diseases: From SIR Models to Diffusion-Based Approaches and Numerical SolutionsAyesha Baig, Zhouxin Li — 2025
• Theoretical Analysis of Canonical Midpoint Splitting Method for Stiff Functional Differential-Algebraic EquationsHaodong Li, Hongliang Liu, Tan Tan — 2025

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