Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions
An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the...
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| Format: | Article |
| Language: | English |
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Vilnius Gediminas Technical University
2021-05-01
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| Series: | Mathematical Modelling and Analysis |
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| Online Access: | https://journals.vgtu.lt/index.php/MMA/article/view/12865 |
| _version_ | 1818878883738419200 |
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| author | Abdeldjalil Chattouh Khaled Saoudi |
| author_facet | Abdeldjalil Chattouh Khaled Saoudi |
| author_sort | Abdeldjalil Chattouh |
| collection | DOAJ |
| description | An efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results. |
| first_indexed | 2024-12-19T14:21:16Z |
| format | Article |
| id | doaj.art-f74e44d4c69a4da39f2a60a4904e26e0 |
| institution | Directory Open Access Journal |
| issn | 1392-6292 1648-3510 |
| language | English |
| last_indexed | 2024-12-19T14:21:16Z |
| publishDate | 2021-05-01 |
| publisher | Vilnius Gediminas Technical University |
| record_format | Article |
| series | Mathematical Modelling and Analysis |
| spelling | doaj.art-f74e44d4c69a4da39f2a60a4904e26e02022-12-21T20:17:46ZengVilnius Gediminas Technical UniversityMathematical Modelling and Analysis1392-62921648-35102021-05-0126210.3846/mma.2021.12865Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditionsAbdeldjalil Chattouh0Khaled Saoudi1ICOSI Laboratory, Department of Mathematics and Informatics, Faculty of Sciences and Technology University Khenchela, P.O. Box 1252, 40004 Khenchela, AlgeriaICOSI Laboratory, Department of Mathematics and Informatics, Faculty of Sciences and Technology University Khenchela, P.O. Box 1252, 40004 Khenchela, AlgeriaAn efficient Legendre-Galerkin spectral method and its error analysis for a one-dimensional parabolic equation with Dirichlet-type non-local boundary conditions are presented in this paper. The spatial discretization is based on Galerkin formulation and the Legendre orthogonal polynomials, while the time derivative is discretized by using the symmetric Euler finite difference schema. The stability and convergence of the semi-discrete spectral approximation are rigorously set up by following a novel approach to overcome difficulties caused by the non-locality of the boundary condition. Several numerical tests are included to confirm the efficacy of the proposed method and to support the theoretical results.https://journals.vgtu.lt/index.php/MMA/article/view/12865spectral methodsGalerkin methodparabolic equationnon-local boundary conditionserror estimate |
| spellingShingle | Abdeldjalil Chattouh Khaled Saoudi Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions Mathematical Modelling and Analysis spectral methods Galerkin method parabolic equation non-local boundary conditions error estimate |
| title | Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions |
| title_full | Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions |
| title_fullStr | Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions |
| title_full_unstemmed | Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions |
| title_short | Error analysis of Legendre-Galerkin spectral method for a parabolic equation with Dirichlet-Type non-local boundary conditions |
| title_sort | error analysis of legendre galerkin spectral method for a parabolic equation with dirichlet type non local boundary conditions |
| topic | spectral methods Galerkin method parabolic equation non-local boundary conditions error estimate |
| url | https://journals.vgtu.lt/index.php/MMA/article/view/12865 |
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