Numerical methods for time-dependent convection-diffusion equations
Journal of Computational and Applied Mathematics
Journal of Computational Physics
Applied Numerical Mathematics
Fitted Numerical Methods for Singular Perturbation Problems: Error Estimates in the Maximum Norm for Linear Problems in One and Two Dimensions
Journal of Computational and Applied Mathematics
International Journal of Computer Mathematics
An efficient numerical scheme for singularly perturbed parabolic problems with interior layer
Neural, Parallel & Scientific Computations
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In this paper we construct a numerical method to solve one-dimensional time-dependent convection-diffusion problem with dominating convection term. We use the classical Euler implicit method for the time discretization and the simple upwind scheme on a special nonuniform mesh for the spatial discretization. We show that the resulting method is uniformly convergent with respect to the diffusion parameter. The main lines for the analysis of the uniform convergence carried out here can be used for the study of more general singular perturbation problems and also for more complicated numerical schemes. The numerical results show that, in practice, some of the theoretical compatibility conditions seem not necessary.