Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations
In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establish...
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| Format: | Article |
| Language: | English |
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Wiley
2020-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2020/7254254 |
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| _version_ | 1850216523795267584 |
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| author | Yameng Wang Juan Zhang Yufeng Sun |
| author_facet | Yameng Wang Juan Zhang Yufeng Sun |
| author_sort | Yameng Wang |
| collection | DOAJ |
| description | In this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method. |
| format | Article |
| id | doaj-art-3bca4603ad7b42c2b914dcd1ea8ac72c |
| institution | OA Journals |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2020-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-3bca4603ad7b42c2b914dcd1ea8ac72c2025-08-20T02:08:16ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2020-01-01202010.1155/2020/72542547254254Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential EquationsYameng Wang0Juan Zhang1Yufeng Sun2College of Mathematics and Information Science, Hebei University, Baoding 071002, ChinaCollege of Mathematics and Information Science, Hebei University, Baoding 071002, ChinaSchool of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, ChinaIn this paper, we investigate the convergence of approximate solutions for a class of first-order integro-differential equations with antiperiodic boundary value conditions. By introducing the definitions of the coupled lower and upper solutions which are different from the former ones and establishing some new comparison principles, the results of the existence and uniqueness of solutions of the problem are given. Finally, we obtain the uniform and rapid convergence of the iterative sequences of approximate solutions via the coupled lower and upper solutions and quasilinearization method. In addition, an example is given to illustrate the feasibility of the method.http://dx.doi.org/10.1155/2020/7254254 |
| spellingShingle | Yameng Wang Juan Zhang Yufeng Sun Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations Discrete Dynamics in Nature and Society |
| title | Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations |
| title_full | Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations |
| title_fullStr | Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations |
| title_full_unstemmed | Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations |
| title_short | Convergence of Antiperiodic Boundary Value Problems for First-Order Integro-Differential Equations |
| title_sort | convergence of antiperiodic boundary value problems for first order integro differential equations |
| url | http://dx.doi.org/10.1155/2020/7254254 |
| work_keys_str_mv | AT yamengwang convergenceofantiperiodicboundaryvalueproblemsforfirstorderintegrodifferentialequations AT juanzhang convergenceofantiperiodicboundaryvalueproblemsforfirstorderintegrodifferentialequations AT yufengsun convergenceofantiperiodicboundaryvalueproblemsforfirstorderintegrodifferentialequations |