A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions
This paper is devoted to develop a new matrix scheme for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. We first transform these equations into equivalent integro partial differential equations (PDEs). Such these integro-PDEs contain both of the initia...
محفوظ في:
| المؤلف الرئيسي: | |
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| مؤلفون آخرون: | |
| منشور في: |
2016
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| الوصول للمادة أونلاين: | http://www.sciencedirect.com/science/journal/00963003/291/supp/C http://hdl.handle.net/11675/3031 |
| الوسوم: |
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| _version_ | 1870679725943291904 |
|---|---|
| author | Zogheib, Bashar |
| author2 | Tohidi, Emran |
| author2_role | author |
| author_facet | Zogheib, Bashar Tohidi, Emran |
| author_role | author |
| dc.creator.none.fl_str_mv | Zogheib, Bashar Tohidi, Emran |
| dc.date.none.fl_str_mv | 2016 2017-10-02T07:39:09Z 2017-10-02T07:39:09Z |
| dc.identifier.none.fl_str_mv | http://www.sciencedirect.com/science/journal/00963003/291/supp/C http://hdl.handle.net/11675/3031 |
| dc.relation.none.fl_str_mv | Applied Mathematics and Computation |
| dc.title.none.fl_str_mv | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| dc.type.none.fl_str_mv | Journal Article Peer-Reviewed info:eu-repo/semantics/publishedVersion |
| description | This paper is devoted to develop a new matrix scheme for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. We first transform these equations into equivalent integro partial differential equations (PDEs). Such these integro-PDEs contain both of the initial and boundary conditions and can be solved numerically in a more appropriate manner. Subsequently, all the existing known and unknown functions in the latter equations are approximated by Bernoulli polynomials and operational matrices of differentiation and integration together with the completeness of these polynomials can be used to reduce the integro-PDEs into the associated algebraic generalized Sylvester equations. For solving these algebraic equations, an efficient Krylov subspace iterative method (i.e., BICGSTAB) is implemented. Two numerical examples are given to demonstrate the efficiency, accuracy, and versatility of the proposed method. |
| id | AUKR_f7fba9fbf67b62ca3ac8a26c5eb08447 |
| network_acronym_str | AUKR |
| network_name_str | AU Kuwait Rep |
| oai_identifier_str | oai:dspace.auk.edu.kw:11675/3031 |
| publishDate | 2016 |
| repository.mail.fl_str_mv | |
| repository.name.fl_str_mv | |
| repository_id_str | |
| spelling | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditionsZogheib, BasharTohidi, EmranThis paper is devoted to develop a new matrix scheme for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions. We first transform these equations into equivalent integro partial differential equations (PDEs). Such these integro-PDEs contain both of the initial and boundary conditions and can be solved numerically in a more appropriate manner. Subsequently, all the existing known and unknown functions in the latter equations are approximated by Bernoulli polynomials and operational matrices of differentiation and integration together with the completeness of these polynomials can be used to reduce the integro-PDEs into the associated algebraic generalized Sylvester equations. For solving these algebraic equations, an efficient Krylov subspace iterative method (i.e., BICGSTAB) is implemented. Two numerical examples are given to demonstrate the efficiency, accuracy, and versatility of the proposed method.2017-10-02T07:39:09Z2017-10-02T07:39:09Z2016Journal ArticlePeer-Reviewedinfo:eu-repo/semantics/publishedVersionhttp://www.sciencedirect.com/science/journal/00963003/291/supp/Chttp://hdl.handle.net/11675/3031Applied Mathematics and Computationoai:dspace.auk.edu.kw:11675/30312022-01-13T09:22:04Z |
| spellingShingle | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions Zogheib, Bashar |
| status_str | publishedVersion |
| title | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| title_full | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| title_fullStr | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| title_full_unstemmed | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| title_short | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| title_sort | A new matrix method for solving two-dimensional time-dependent diffusion equations with Dirichlet boundary conditions |
| url | http://www.sciencedirect.com/science/journal/00963003/291/supp/C http://hdl.handle.net/11675/3031 |