A Stable Numerical Approach for Implicit Non-Linear Neutral Delay Differential Equations

Keywords

Mathematics, Stability (learning theory), Forcing (mathematics), Applied mathematics, Term (time)

References

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• Asymptotic stability analysis of Runge-Kutta methods for nonlinear systems of delay differential equationsMarino Zennaro — 1997
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• Stability analysis of numerical methods for systems of neutral delay-differential equationsGuang‐Da Hu, Taketomo Mitsui — 1995
• Retarded differential equationsChristopher Baker — 2000
• A class of functional equations of neutral typeJack K. Hale, Kenneth R. Meyer — 1967
• Numerical Solution of Implicit Neutral Functional Differential EquationsYunkang Liu — 1999
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• Theory of Functional Differential EquationsJack K. Hale — 1977
• Applied Theory of Functional Differential EquationsV. Kolmanovskii, A. Myshkis — 1992
• The numerical solution of delay-differential-algebraic equations of retarded and neutral typeUri M. Ascher, Linda Petzold — 1995
• Stability and Asymptotic Stability of Functional‐Differential EquationsArieh Iserles, József Terjéki — 1995
• Time domain solutions for coupled problems using PEEC models with waveform relaxationW. Pinello, Albert E. Ruehli — 1996
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Cited by

• Stability Analysis of One-Leg Methods for Nonlinear Neutral Delay Integrodifferential EquationsYuexin Yu, Liping Wen — 2015
• Theory and numerical analysis of Volterra functional equationsHermann Brunner — 2008
• High-order collocation methods for singular Volterra functional equations of neutral typeHermann Brunner — 2007
• Stepsize Restrictions for Nonlinear Stability Properties of Neutral Delay Differential EquationsWei Gu, Ming Wang, Dongfang Li — 2014
• Nonlinear stability of Runge-Kutta methods for neutral delay differential equationsWansheng Wang, Shoufu Li, Kai Su — 2008
• Stability Analysis of Runge-Kutta Methods for Nonlinear Functional Differential and Functional EquationsYuexin Yu, Zhongyan Liu, Liping Wen — 2014
• Stability of continuous Runge–Kutta-type methods for nonlinear neutral delay-differential equationsWansheng Wang, Yuan Zhang, Shoufu Li — 2009
• Stability of linear multistep methods for nonlinear neutral delay differential equations in Banach spaceWansheng Wang, Liping Wen, Shoufu Li — 2010
• Transient growth of Görtler vortices in two-dimensional compressible boundary layers. Application to surface wavinessJean-Michel Lucas, Olivier Vermeersch, D. Arnal — 2015
• Nonlinear stability of explicit and diagonally implicit Runge-Kutta methods for neutral delay differential equations in Banach spaceWansheng Wang, Liping Wen, Shoufu Li — 2008
• Nonlinear stability of Runge-Kutta methods for neutral delay integro-differential equationsYuexin Yu, Liping Wen, Shoufu Li — 2007
• Nonlinear stability of one-leg methods for delay differential equations of neutral typeWansheng Wang, Yuan Zhang, Shoufu Li — 2008
• Dissipativity of θ-methods for nonlinear delay differential equations of neutral typeSiqing Gan — 2009
• The extended Pouzet–Runge–Kutta methods for nonlinear neutral delay-integro-differential equationsChengjian Zhang, Tingting Qin, Jie Jin — 2010
• Stability analysis of general linear methods for nonlinear neutral delay differential equationsYuexin Yu, Liping Wen, Shoufu Li — 2007
• Stability Analysis of Theta-Methods for Nonlinear Neutral Functional Differential EquationsWansheng Wang, Shoufu Li — 2008
• Numerical stability of one-leg methods for neutral delay differential equationsLiping Wen, Xiong Liu — 2012
• Nonlinear stability of general linear methods for neutral delay differential equationsWansheng Wang, Shoufu Li, Kai Su — 2009
• Stability of solutions of delay functional integro-differential equations and their discretizationsHermann Brunner, Rossana Vermiglio — 2003
• Conditional contractivity of Runge–Kutta methods for nonlinear differential equations with many variable delays☆Wansheng Wang, Shoufu Li — 2009

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