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.
@article{28664,
title = {A numerical method for solving time-dependent convection-diffusion problems},
journal = {Boletim da Sociedade Paranaense de Matem\'atica},
volume = {34},
year = {2015},
doi = {10.5269/bspm.v35i1.28664},
language = {EN},
url = {http://dml.mathdoc.fr/item/28664}
}
El Hajaji, Abdelmajid. A numerical method for solving time-dependent convection-diffusion problems. Boletim da Sociedade Paranaense de Matemática, Tome 34 (2015) . doi : 10.5269/bspm.v35i1.28664. http://gdmltest.u-ga.fr/item/28664/