Robust novel high‐order accurate numerical methods for singularly perturbed convection‐diffusion problems
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.
Stiprūs nauji aukštos eilės tikslūs skaitmeniniai metodai singuliariai sutrukdytiems konvekcijos-difuzijos uždaviniams
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
Keywords:
singular perturbation, boundary layer, parabolic convection‐diffusion equation, difference scheme, parameter‐uniform convergence, high‐order accuracyHow to Cite
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Copyright (c) 2005 The Author(s). Published by Vilnius Gediminas Technical University.
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Copyright (c) 2005 The Author(s). Published by Vilnius Gediminas Technical University.
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This work is licensed under a Creative Commons Attribution 4.0 International License.