Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t])
This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′(t)=au(t)+bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. Th...
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| Main Authors: | , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2012-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2012/125926 |
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| _version_ | 1832550384241999872 |
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| author | Han Yan Shufang Ma Yanbin Liu Hongquan Sun |
| author_facet | Han Yan Shufang Ma Yanbin Liu Hongquan Sun |
| author_sort | Han Yan |
| collection | DOAJ |
| description | This paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′(t)=au(t)+bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given. |
| format | Article |
| id | doaj-art-e1d42047df89471ab825b8e160afa01d |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2012-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-e1d42047df89471ab825b8e160afa01d2025-02-03T06:06:59ZengWileyJournal of Applied Mathematics1110-757X1687-00422012-01-01201210.1155/2012/125926125926Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t])Han Yan0Shufang Ma1Yanbin Liu2Hongquan Sun3School of Mathematical Sciences, Heilongjiang University, Harbin 150080, ChinaDepartment of Mathematics, Northeast Forest University, Harbin 150040, ChinaSchool of Mathematical Sciences, Heilongjiang University, Harbin 150080, ChinaSchool of Mathematical Sciences, Heilongjiang University, Harbin 150080, ChinaThis paper is concerned with the convergence, global superconvergence, local superconvergence, and stability of collocation methods for u′(t)=au(t)+bu([t]). The optimal convergence order and superconvergence order are obtained, and the stability regions for the collocation methods are determined. The conditions that the analytic stability region is contained in the numerical stability region are obtained, and some numerical experiments are given.http://dx.doi.org/10.1155/2012/125926 |
| spellingShingle | Han Yan Shufang Ma Yanbin Liu Hongquan Sun Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) Journal of Applied Mathematics |
| title | Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) |
| title_full | Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) |
| title_fullStr | Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) |
| title_full_unstemmed | Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) |
| title_short | Convergence and Stability in Collocation Methods of Equation u′(t)=au(t)+bu([t]) |
| title_sort | convergence and stability in collocation methods of equation u t au t bu t |
| url | http://dx.doi.org/10.1155/2012/125926 |
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