Finite element approximation of fractional hyperbolic integro-differential equation
In this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element met...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2022-06-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2022841?viewType=HTML |
| _version_ | 1817979390847352832 |
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| author | Zhengang Zhao Yunying Zheng Xianglin Zeng |
| author_facet | Zhengang Zhao Yunying Zheng Xianglin Zeng |
| author_sort | Zhengang Zhao |
| collection | DOAJ |
| description | In this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element method in spatial direction, we apply a second order symmetric difference method in time. Next we discuss the regularity analysis of the weak solution and convergence analysis of the semi-discrete scheme. Then we further study the stability analysis and the error estimation of the fully discrete problems, according to the properties of fractional Ritz-Volterra projection, Ritz projection and so on. Numerical examples with comparisons among the proposed schemes verify our theoretical analyses. |
| first_indexed | 2024-04-13T22:42:10Z |
| format | Article |
| id | doaj.art-be233d1676df40ce892aaa197e820d40 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-13T22:42:10Z |
| publishDate | 2022-06-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-be233d1676df40ce892aaa197e820d402022-12-22T02:26:35ZengAIMS PressAIMS Mathematics2473-69882022-06-0178153481536910.3934/math.2022841Finite element approximation of fractional hyperbolic integro-differential equationZhengang Zhao0Yunying Zheng1Xianglin Zeng 21. Department of Fundamental Courses, Shanghai Customs College, Shanghai 201204, China2. School of Mathematical Sciences, Huaibei Normal University, Huaibei 235000, China3. Academic Adminstration, Shanghai Customs College, Shanghai 201204, ChinaIn this article, we propose a Galerkin finite element method for numerically solving a type of fractional hyperbolic integro-differential equation, which can be considered as the generalization of the classical hyperbolic Volterra integro-differential equation. Along with Galerkin finite element method in spatial direction, we apply a second order symmetric difference method in time. Next we discuss the regularity analysis of the weak solution and convergence analysis of the semi-discrete scheme. Then we further study the stability analysis and the error estimation of the fully discrete problems, according to the properties of fractional Ritz-Volterra projection, Ritz projection and so on. Numerical examples with comparisons among the proposed schemes verify our theoretical analyses.https://www.aimspress.com/article/doi/10.3934/math.2022841?viewType=HTMLfractional hyperbolic integro-differential equationfractional derivativefractional ritz-volterra projectiongalerkin finite element method |
| spellingShingle | Zhengang Zhao Yunying Zheng Xianglin Zeng Finite element approximation of fractional hyperbolic integro-differential equation AIMS Mathematics fractional hyperbolic integro-differential equation fractional derivative fractional ritz-volterra projection galerkin finite element method |
| title | Finite element approximation of fractional hyperbolic integro-differential equation |
| title_full | Finite element approximation of fractional hyperbolic integro-differential equation |
| title_fullStr | Finite element approximation of fractional hyperbolic integro-differential equation |
| title_full_unstemmed | Finite element approximation of fractional hyperbolic integro-differential equation |
| title_short | Finite element approximation of fractional hyperbolic integro-differential equation |
| title_sort | finite element approximation of fractional hyperbolic integro differential equation |
| topic | fractional hyperbolic integro-differential equation fractional derivative fractional ritz-volterra projection galerkin finite element method |
| url | https://www.aimspress.com/article/doi/10.3934/math.2022841?viewType=HTML |
| work_keys_str_mv | AT zhengangzhao finiteelementapproximationoffractionalhyperbolicintegrodifferentialequation AT yunyingzheng finiteelementapproximationoffractionalhyperbolicintegrodifferentialequation AT xianglinzeng finiteelementapproximationoffractionalhyperbolicintegrodifferentialequation |