Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations
Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDE...
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| Format: | Article |
| Language: | English |
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Wiley
2021-01-01
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| Series: | Discrete Dynamics in Nature and Society |
| Online Access: | http://dx.doi.org/10.1155/2021/6633554 |
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| author | Yunfei Li Shoufu Li |
| author_facet | Yunfei Li Shoufu Li |
| author_sort | Yunfei Li |
| collection | DOAJ |
| description | Based on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories. |
| format | Article |
| id | doaj-art-30176f7eb18f4d9291a83bca12e9c251 |
| institution | Kabale University |
| issn | 1026-0226 1607-887X |
| language | English |
| publishDate | 2021-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Discrete Dynamics in Nature and Society |
| spelling | doaj-art-30176f7eb18f4d9291a83bca12e9c2512025-02-03T06:05:26ZengWileyDiscrete Dynamics in Nature and Society1026-02261607-887X2021-01-01202110.1155/2021/66335546633554Classical Theory of Linear Multistep Methods for Volterra Functional Differential EquationsYunfei Li0Shoufu Li1College of Mathematics and Physics, Hunan Province Cooperative Innovation Center for the Construction and Development of Dongting Lake Ecological Economic Zone, Hunan University of Arts and Science, Changde 415000, Hunan, ChinaDepartment of Mathematics, Xiangtan University, Xiangtan 411105, ChinaBased on the linear multistep methods for ordinary differential equations (ODEs) and the canonical interpolation theory that was presented by Shoufu Li who is exactly the second author of this paper, we propose the linear multistep methods for general Volterra functional differential equations (VFDEs) and build the classical stability, consistency, and convergence theories of the methods. The methods and theories presented in this paper are applicable to nonneutral, nonstiff, and nonlinear initial value problems in ODEs, Volterra delay differential equations (VDDEs), Volterra integro-differential equations (VIDEs), Volterra delay integro-differential equations (VDIDEs), etc. At last, some numerical experiments verify the correctness of our theories.http://dx.doi.org/10.1155/2021/6633554 |
| spellingShingle | Yunfei Li Shoufu Li Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations Discrete Dynamics in Nature and Society |
| title | Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations |
| title_full | Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations |
| title_fullStr | Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations |
| title_full_unstemmed | Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations |
| title_short | Classical Theory of Linear Multistep Methods for Volterra Functional Differential Equations |
| title_sort | classical theory of linear multistep methods for volterra functional differential equations |
| url | http://dx.doi.org/10.1155/2021/6633554 |
| work_keys_str_mv | AT yunfeili classicaltheoryoflinearmultistepmethodsforvolterrafunctionaldifferentialequations AT shoufuli classicaltheoryoflinearmultistepmethodsforvolterrafunctionaldifferentialequations |