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- W2912456117 abstract "On the set (overline{G} =G cup S), (G=(0,d]times (0,T]) with the boundary (S=S_0 cup S^{,ell }), we consider an initial-boundary value problem for the singularly perturbed transport equation with a perturbation parameter (varepsilon ) multiplying the spatial derivative, (varepsilon in (0,1]). For small values of the perturbation parameter (varepsilon ), the solution of such a problem has a singularity of the boundary layer type, which makes standard difference schemes unsuitable for practical computations. To solve this problem numerically, an approach to the development of a robust difference scheme is proposed, similar to that used for constructing special (varepsilon )-uniformly convergent difference schemes for singularly perturbed elliptic and parabolic equations. In this paper, we give a technique for constructing a robust difference scheme and justifying its (varepsilon )-uniform convergence, and we study numerically solutions of standard and special robust difference schemes for a model initial-boundary value problem for a singularly perturbed transport equation. The results of numerical experiments confirm theoretical results." @default.
- W2912456117 created "2019-02-21" @default.
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- W2912456117 date "2019-01-01" @default.
- W2912456117 modified "2023-09-25" @default.
- W2912456117 title "Development and Numerical Study of Robust Difference Schemes for a Singularly Perturbed Transport Equation" @default.
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- W2912456117 doi "https://doi.org/10.1007/978-3-030-11539-5_55" @default.
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