Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions
The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be s...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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Sciendo
2020-12-01
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| Series: | Moroccan Journal of Pure and Applied Analysis |
| Subjects: | |
| Online Access: | https://doi.org/10.2478/mjpaa-2020-0023 |
| _version_ | 1828872673539653632 |
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| author | Chattouh Abdeldjalil Saoudi Khaled |
| author_facet | Chattouh Abdeldjalil Saoudi Khaled |
| author_sort | Chattouh Abdeldjalil |
| collection | DOAJ |
| description | The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in L2-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method. |
| first_indexed | 2024-12-13T06:59:12Z |
| format | Article |
| id | doaj.art-80363cd38fdf42519f0fbd2d7d513bf2 |
| institution | Directory Open Access Journal |
| issn | 2351-8227 |
| language | English |
| last_indexed | 2024-12-13T06:59:12Z |
| publishDate | 2020-12-01 |
| publisher | Sciendo |
| record_format | Article |
| series | Moroccan Journal of Pure and Applied Analysis |
| spelling | doaj.art-80363cd38fdf42519f0fbd2d7d513bf22022-12-21T23:55:58ZengSciendoMoroccan Journal of Pure and Applied Analysis2351-82272020-12-016230331710.2478/mjpaa-2020-0023Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditionsChattouh Abdeldjalil0Saoudi Khaled1Department of Mathematics and Informatics, ICOSI Laboratory, Abbes Laghrour University, Khenchela, BP 1252 Road of Batna Khenchela 40004, Algeria.Department of Mathematics and Informatics, ICOSI Laboratory, Abbes Laghrour University, Khenchela, BP 1252 Road of Batna Khenchela 40004, Algeria.The present paper is devoted to the numerical approximation for the diffusion equation subject to non-local boundary conditions. For the space discretization, we apply the Legendre-Chebyshev pseudospectral method, so that, the problem under consideration is reduced to a system of ODEs which can be solved by the second order Crank-Nicolson schema. Optimal error estimates for the semi-discrete scheme are derived in L2-norm. Numerical tests are included to demonstrate the effectiveness of the proposed method.https://doi.org/10.2478/mjpaa-2020-0023numerical solutionpseudo-spectral methodparabolic equationnon-local boundary conditionserror estimate65m7065m1265n3535k20 |
| spellingShingle | Chattouh Abdeldjalil Saoudi Khaled Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions Moroccan Journal of Pure and Applied Analysis numerical solution pseudo-spectral method parabolic equation non-local boundary conditions error estimate 65m70 65m12 65n35 35k20 |
| title | Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions |
| title_full | Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions |
| title_fullStr | Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions |
| title_full_unstemmed | Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions |
| title_short | Legendre-Chebyshev pseudo-spectral method for the diffusion equation with non-classical boundary conditions |
| title_sort | legendre chebyshev pseudo spectral method for the diffusion equation with non classical boundary conditions |
| topic | numerical solution pseudo-spectral method parabolic equation non-local boundary conditions error estimate 65m70 65m12 65n35 35k20 |
| url | https://doi.org/10.2478/mjpaa-2020-0023 |
| work_keys_str_mv | AT chattouhabdeldjalil legendrechebyshevpseudospectralmethodforthediffusionequationwithnonclassicalboundaryconditions AT saoudikhaled legendrechebyshevpseudospectralmethodforthediffusionequationwithnonclassicalboundaryconditions |