Open AccessHIGH-ORDER DIFFERENCE SCHEMES FOR CONVECTION‐DIFFUSION INTERFACE PROBLEMS
Author(s) -
Ivanka Tr. Angelova
Publication year - 2005
Publication title -
mathematical modelling and analysis/mathematical modeling and analysis
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.491
H-Index - 25
eISSN - 1648-3510
pISSN - 1392-6292
DOI - 10.3846/13926292.2005.9637290
Subject(s) - quadrature (astronomy) , mathematics , diffusion , mathematical analysis , physics , thermodynamics , optics
On non‐uniform mesh new high‐order compact finite difference approximations of the solution and the flux to convection‐diffusion interface problems in one‐dimension are constructed and analyzed. Explicit formulas based on new Marchuk integral identities that give O(h2), O(h4), . . . accuracy are derived. New numerical integration quadrature procedures for computing three‐point schemes of any prescribed order of accuracy are developed. Numerical experiments confirm the theoretical results.Straipsnyje sukonstruotos ir analizuojamos naujos aukštos eiles kompaktines baigtiniu skirtumu schemos, aproksimuojančios konvekcijos‐difuzijos saveikos uždavinius vienmačiu atveju. Gautos išreikštines O(h 2), O(h4), … eiles tikslumo formules, pagristos Marchuko integralinemis tapatybemis. Išvestos naujos skaitmeninio integravimo kvadratūrines nurodyto tikslumo formules tritaškiu schemu skaičiavimui. Pateikti skaitiniai eksperimentai, patvirtinantys teorinius rezultatus.