The a posteriori error estimate in fractional differential equations using generalized Jacobi functions
In this work, we study a posteriori error analysis of a general class of fractional initial value problems and fractional boundary value problems. A Petrov-Galerkin spectral method is adopted as the discretization technique in which the generalized Jacobi functions are utilized as basis functions fo...
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
AIMS Press
2023-10-01
|
| Series: | AIMS Mathematics |
| Subjects: | |
| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.20231486?viewType=HTML |
| _version_ | 1797635369338929152 |
|---|---|
| author | Bo Tang Huasheng Wang |
| author_facet | Bo Tang Huasheng Wang |
| author_sort | Bo Tang |
| collection | DOAJ |
| description | In this work, we study a posteriori error analysis of a general class of fractional initial value problems and fractional boundary value problems. A Petrov-Galerkin spectral method is adopted as the discretization technique in which the generalized Jacobi functions are utilized as basis functions for constructing efficient spectral approximations. The unique solvability of the weak problems is established by verifying the Babuška-Brezzi inf-sup condition. Then, we introduce some residual-type a posteriori error estimators, and deduce their efficiency and reliability in properly weighted Sobolev space. Numerical examples are given to illustrate the performance of the obtained error estimators. |
| first_indexed | 2024-03-11T12:20:08Z |
| format | Article |
| id | doaj.art-bf17270a691443a5ab4912353d403f38 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-03-11T12:20:08Z |
| publishDate | 2023-10-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-bf17270a691443a5ab4912353d403f382023-11-07T01:46:22ZengAIMS PressAIMS Mathematics2473-69882023-10-01812290172904110.3934/math.20231486The a posteriori error estimate in fractional differential equations using generalized Jacobi functionsBo Tang0Huasheng Wang11. School of Mathematics and Information Science, Guangzhou University, Guangzhou 510006, Guangdong, China2. School of Mathematics and Computational Science, Wuyi University, Jiangmen, 529020, Guangdong, ChinaIn this work, we study a posteriori error analysis of a general class of fractional initial value problems and fractional boundary value problems. A Petrov-Galerkin spectral method is adopted as the discretization technique in which the generalized Jacobi functions are utilized as basis functions for constructing efficient spectral approximations. The unique solvability of the weak problems is established by verifying the Babuška-Brezzi inf-sup condition. Then, we introduce some residual-type a posteriori error estimators, and deduce their efficiency and reliability in properly weighted Sobolev space. Numerical examples are given to illustrate the performance of the obtained error estimators.https://www.aimspress.com/article/doi/10.3934/math.20231486?viewType=HTMLfractional initial value problemsfractional boundary value problemsgeneralized jacobi functionspetrov-galerkin spectral methodsa posteriori error estimators |
| spellingShingle | Bo Tang Huasheng Wang The a posteriori error estimate in fractional differential equations using generalized Jacobi functions AIMS Mathematics fractional initial value problems fractional boundary value problems generalized jacobi functions petrov-galerkin spectral methods a posteriori error estimators |
| title | The a posteriori error estimate in fractional differential equations using generalized Jacobi functions |
| title_full | The a posteriori error estimate in fractional differential equations using generalized Jacobi functions |
| title_fullStr | The a posteriori error estimate in fractional differential equations using generalized Jacobi functions |
| title_full_unstemmed | The a posteriori error estimate in fractional differential equations using generalized Jacobi functions |
| title_short | The a posteriori error estimate in fractional differential equations using generalized Jacobi functions |
| title_sort | a posteriori error estimate in fractional differential equations using generalized jacobi functions |
| topic | fractional initial value problems fractional boundary value problems generalized jacobi functions petrov-galerkin spectral methods a posteriori error estimators |
| url | https://www.aimspress.com/article/doi/10.3934/math.20231486?viewType=HTML |
| work_keys_str_mv | AT botang theaposteriorierrorestimateinfractionaldifferentialequationsusinggeneralizedjacobifunctions AT huashengwang theaposteriorierrorestimateinfractionaldifferentialequationsusinggeneralizedjacobifunctions AT botang aposteriorierrorestimateinfractionaldifferentialequationsusinggeneralizedjacobifunctions AT huashengwang aposteriorierrorestimateinfractionaldifferentialequationsusinggeneralizedjacobifunctions |