In the present paper the difference schemes of high order accuracy for two‐dimensional equations of mathematical physics in an arbitrary domain are constructed. The computational domain is covered by a uniform rectangular grid. The second order accuracy of local approximation by spatial variables is achieved near‐boundary nodes. No increase of a standard grid scheme template is required. A priori estimates of the stability are obtained.
Didelio tikslumo baigtinių skirtumų schemos
Santrauka. Darbe nagrinėjami matematines fizikos uždaviniai, kai apibrėžimo srities kontūras yra bet kokia glodi uždara kreivė. Ši sritis pakeičiama tolygiu stačiakampiu tinklu. Panaudojant specialias aproksimavimo formules ir pasienio taškuose aproksimacijos paklaidos eilė yra antroji. Svarbi naujojo algoritmo savybė yra tai, kad visuose taškuose naudojamas toks pat diskrečiojo tinklo šablonas. Įrodomi aprioriniai stabilumo įverčiai ir įvertinamas diskrečiojo sprendinio konvergavimo greitis. Pateikti skaičiavimo eksperimento, kuriame naujoji schema palyginama su dviem kitomis žinomomis baigtinių skirtumų schemomis, rezultatai.
Matus, P. P., & Zyl, A. N. (2000). Difference schemes of high order accuracy for mathematical physics problems in arbitrary domains. Mathematical Modelling and Analysis, 5(1), 133-142. https://doi.org/10.3846/13926292.2000.9637136
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