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.
Aukštos eilė skirtumų schemos konvekcijos-difuzijos sąveikos uždaviniams
Straipsnyje sukonstruotos ir analizuojamos naujos aukštos eilės kompaktinės baigtinių skirtumų schemos, aproksimuojančios konvekcijos‐difuzijos sąveikos uždavinius vienmačiu atveju. Gautos išreikštinės O(h2), O(h4), … eilės tikslumo formulės, pagrįstos Marchuko integralinėmis tapatybėmis. Išvestos naujos skaitmeninio integravimo kvadratūrinės nurodyto tikslumo formulės tritaškių schemų skaičiavimui. Pateikti skaitiniai eksperimentai, patvirtinantys teorinius rezultatus.
Angelova, I. T. (2005). High‐order difference schemes for convection‐diffusion interface problems. Mathematical Modelling and Analysis, 10(4), 319-334. https://doi.org/10.3846/13926292.2005.9637290
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