A numerical method for solving time-dependent convection-diffusion problems
In this paper, we develop a new numerical method for solving a timedependent convection-diffusion equation with Dirichlet’s type boundary conditions. We first propose the theta-method to discretize the temporal variable, resulting in a linear partial differential equation (PDE). To numerically solve...
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Sociedade Brasileira de Matemática
2017-10-01
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Online Access: | http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/28664 |
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doaj-bfe44a4a3c994fcea1c9b41e1f0e13eb2020-11-24T23:52:07ZengSociedade Brasileira de MatemáticaBoletim da Sociedade Paranaense de Matemática0037-87122175-11882017-10-0135121722810.5269/bspm.v35i1.2866412997A numerical method for solving time-dependent convection-diffusion problemsAbdelmajid El HajajiIn this paper, we develop a new numerical method for solving a timedependent convection-diffusion equation with Dirichlet’s type boundary conditions. We first propose the theta-method to discretize the temporal variable, resulting in a linear partial differential equation (PDE). To numerically solve this linear PDE, we develop and we analyze a new cubic spline collocation method for the spatial discretization. To solve the discretized linear system, we design a collocation method and we prove that the method is second order convergent. The computed results are compared wherever possible with those already available in the literature.http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/28664Convection-diffusion equation, theta-method, Spline collocation method. |
collection |
DOAJ |
language |
English |
format |
Article |
sources |
DOAJ |
author |
Abdelmajid El Hajaji |
spellingShingle |
Abdelmajid El Hajaji A numerical method for solving time-dependent convection-diffusion problems Boletim da Sociedade Paranaense de Matemática Convection-diffusion equation, theta-method, Spline collocation method. |
author_facet |
Abdelmajid El Hajaji |
author_sort |
Abdelmajid El Hajaji |
title |
A numerical method for solving time-dependent convection-diffusion problems |
title_short |
A numerical method for solving time-dependent convection-diffusion problems |
title_full |
A numerical method for solving time-dependent convection-diffusion problems |
title_fullStr |
A numerical method for solving time-dependent convection-diffusion problems |
title_full_unstemmed |
A numerical method for solving time-dependent convection-diffusion problems |
title_sort |
numerical method for solving time-dependent convection-diffusion problems |
publisher |
Sociedade Brasileira de Matemática |
series |
Boletim da Sociedade Paranaense de Matemática |
issn |
0037-8712 2175-1188 |
publishDate |
2017-10-01 |
description |
In this paper, we develop a new numerical method for solving a timedependent convection-diffusion equation with Dirichlet’s type boundary conditions. We first propose the theta-method to discretize the temporal variable, resulting in a linear partial differential equation (PDE). To numerically solve this linear PDE, we develop and we analyze a new cubic spline collocation method for the spatial discretization. To solve the discretized linear system, we design a collocation method and we prove that the method is second order convergent. The computed results are compared wherever possible with those already available in the literature. |
topic |
Convection-diffusion equation, theta-method, Spline collocation method. |
url |
http://periodicos.uem.br/ojs/index.php/BSocParanMat/article/view/28664 |
work_keys_str_mv |
AT abdelmajidelhajaji anumericalmethodforsolvingtimedependentconvectiondiffusionproblems AT abdelmajidelhajaji numericalmethodforsolvingtimedependentconvectiondiffusionproblems |
_version_ |
1725474797400358912 |