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Robust novel high‐order accurate numerical methods for singularly perturbed convection‐diffusion problems

    G. I. Shishkin Affiliation

Abstract


For singularly perturbed boundary value problems, numerical methods convergent ϵ‐uniformly have the low accuracy. So, for parabolic convection‐diffusion problem the order of convergence does not exceed one even if the problem data are sufficiently smooth. However, already for piecewise smooth initial data this order is not higher than 1/2. For problems of such type, using newly developed methods such as the method based on the asymptotic expansion technique and the method of the additive splitting of singularities, we construct ϵ‐uniformly convergent schemes with improved order of accuracy.



Straipsnyje nagrinejami nedidelio tikslumo ϵ‐tolygiai konvertuojantys skaitmeniniai metodai, singuliariai sutrikdytiems kraštiniams uždaviniams. Paraboliniam konvekcijos‐difuzijos uždaviniui konvergavimo eile neviršija vienos antrosios, jeigu uždavinio duomenys yra pakankamai glodūs. Tačiau trūkiems pradiniams duomenims eile yra ne aukštesne už 2−1. Šio tipo uždaviniams, naudojant naujai išvestus metodus, darbe sukonstruotos ϵ‐tolygiai konvertuojančios schemos aukštesniu tikslumu.


First Published Online: 14 Oct 2010

Keyword : singular perturbation, boundary layer, parabolic convection‐diffusion equation, difference scheme, parameter‐uniform convergence, high‐order accuracy

How to Cite
Shishkin, G. I. (2005). Robust novel high‐order accurate numerical methods for singularly perturbed convection‐diffusion problems. Mathematical Modelling and Analysis, 10(4), 393-412. https://doi.org/10.3846/13926292.2005.9637296
Published in Issue
Dec 31, 2005
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