In the paper elliptic equations with alternating‐sign coefficients at mixed derivatives are considered. For such equations new difference schemes of the second order of approximation are developed. The proposed schemes are conservative and monotone. The constructed algorithms satisfy the grid maximum principle not only for coefficients of constant signs but also for alternating‐sign coefficients at mixed derivatives. The a prioriestimates of stability and convergence in the grid norm C are obtained.
Monotoniškos ir konservatyvios baigtiniu˛ skirtumu˛ schemos eliptinio tipo lygtims su mišriomis išvestinemis
Santrauka. Straipsnyje nagrinėjamos eliptinio tipo lygtys su mišriomis išvestinėmis. Šioms diferencialinėms lygtims pasiūlytos naujos antros eiles baigtinių skirtumų schemos, kurios yra monotoniškos ir konservatyvios. Sukonstruoti algoritmai tenkina skaitinį maksimumo principą, kai koeficientai prie mišriųjų išvestinių gali būti bet kokio ženklo. Gauti aprioriniai įverčiai maksimumo normoje. Įrodyta baigtinių skirtumų schemų stabilumas ir konvergavimas.
Rybak, I. (2004). Monotone and conservative difference schemes for elliptic equations with mixed derivatives. Mathematical Modelling and Analysis, 9(2), 169-178. https://doi.org/10.3846/13926292.2004.9637250
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