Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments
In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the ana...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Wiley
2012-01-01
|
| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/2012/258329 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1832553338799915008 |
|---|---|
| author | Minghui Song M. Z. Liu |
| author_facet | Minghui Song M. Z. Liu |
| author_sort | Minghui Song |
| collection | DOAJ |
| description | In this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the 𝜃-methods are obtained. Some examples are illustrated. |
| format | Article |
| id | doaj-art-82bd2e6e08a3456c86a608b4ae5b26b0 |
| institution | Kabale University |
| issn | 1085-3375 1687-0409 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Abstract and Applied Analysis |
| spelling | doaj-art-82bd2e6e08a3456c86a608b4ae5b26b02025-02-03T05:54:12ZengWileyAbstract and Applied Analysis1085-33751687-04092012-01-01201210.1155/2012/258329258329Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous ArgumentsMinghui Song0M. Z. Liu1Department of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaDepartment of Mathematics, Harbin Institute of Technology, Harbin 150001, ChinaIn this paper, the asymptotic stability of the analytic and numerical solutions for differential equations with piecewise continuous arguments is investigated by using Lyapunov methods. In particular, the linear equations with variable coefficients are considered. The stability conditions of the analytic solutions of those equations and the numerical solutions of the 𝜃-methods are obtained. Some examples are illustrated.http://dx.doi.org/10.1155/2012/258329 |
| spellingShingle | Minghui Song M. Z. Liu Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments Abstract and Applied Analysis |
| title | Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments |
| title_full | Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments |
| title_fullStr | Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments |
| title_full_unstemmed | Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments |
| title_short | Stability of Analytic and Numerical Solutions for Differential Equations with Piecewise Continuous Arguments |
| title_sort | stability of analytic and numerical solutions for differential equations with piecewise continuous arguments |
| url | http://dx.doi.org/10.1155/2012/258329 |
| work_keys_str_mv | AT minghuisong stabilityofanalyticandnumericalsolutionsfordifferentialequationswithpiecewisecontinuousarguments AT mzliu stabilityofanalyticandnumericalsolutionsfordifferentialequationswithpiecewisecontinuousarguments |