Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations
In this paper, the idea of two transformations is first proposed and applied. Some new different sufficient conditions for the asymptotical stability of the exact solutions of nonlinear impulsive neutral delay differential equations (INDDEs) are obtained. A new numerical scheme for INDDEs is also co...
| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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MDPI AG
2023-10-01
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| Series: | Axioms |
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| Online Access: | https://www.mdpi.com/2075-1680/12/10/988 |
| _version_ | 1797574730526490624 |
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| author | Gui-Lai Zhang Zhi-Wei Wang Yang Sun Tao Liu |
| author_facet | Gui-Lai Zhang Zhi-Wei Wang Yang Sun Tao Liu |
| author_sort | Gui-Lai Zhang |
| collection | DOAJ |
| description | In this paper, the idea of two transformations is first proposed and applied. Some new different sufficient conditions for the asymptotical stability of the exact solutions of nonlinear impulsive neutral delay differential equations (INDDEs) are obtained. A new numerical scheme for INDDEs is also constructed based on the idea. The numerical methods that can preserve the stability and asymptotical stability of the exact solutions are provided. Two numerical examples are provided to demonstrate the theoretical results. |
| first_indexed | 2024-03-10T21:26:28Z |
| format | Article |
| id | doaj.art-72760c97e26a45478dd42ebf0f139549 |
| institution | Directory Open Access Journal |
| issn | 2075-1680 |
| language | English |
| last_indexed | 2024-03-10T21:26:28Z |
| publishDate | 2023-10-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Axioms |
| spelling | doaj.art-72760c97e26a45478dd42ebf0f1395492023-11-19T15:38:54ZengMDPI AGAxioms2075-16802023-10-01121098810.3390/axioms12100988Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential EquationsGui-Lai Zhang0Zhi-Wei Wang1Yang Sun2Tao Liu3College of Sciences, Northeastern University, Shenyang 110819, ChinaCollege of Sciences, Northeastern University, Shenyang 110819, ChinaCollege of Sciences, Northeastern University, Shenyang 110819, ChinaCollege of Sciences, Northeastern University, Shenyang 110819, ChinaIn this paper, the idea of two transformations is first proposed and applied. Some new different sufficient conditions for the asymptotical stability of the exact solutions of nonlinear impulsive neutral delay differential equations (INDDEs) are obtained. A new numerical scheme for INDDEs is also constructed based on the idea. The numerical methods that can preserve the stability and asymptotical stability of the exact solutions are provided. Two numerical examples are provided to demonstrate the theoretical results.https://www.mdpi.com/2075-1680/12/10/988Runge–Kutta method<i>BN<sub>f</sub></i>-stableimplicit Euler methodLobatto IIIC method |
| spellingShingle | Gui-Lai Zhang Zhi-Wei Wang Yang Sun Tao Liu Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations Axioms Runge–Kutta method <i>BN<sub>f</sub></i>-stable implicit Euler method Lobatto IIIC method |
| title | Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations |
| title_full | Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations |
| title_fullStr | Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations |
| title_full_unstemmed | Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations |
| title_short | Asymptotical Stability Criteria for Exact Solutions and Numerical Solutions of Nonlinear Impulsive Neutral Delay Differential Equations |
| title_sort | asymptotical stability criteria for exact solutions and numerical solutions of nonlinear impulsive neutral delay differential equations |
| topic | Runge–Kutta method <i>BN<sub>f</sub></i>-stable implicit Euler method Lobatto IIIC method |
| url | https://www.mdpi.com/2075-1680/12/10/988 |
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