Share:


Monotone and conservative difference schemes for elliptic equations with mixed derivatives

    I.V. Rybak Affiliation

Abstract


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 nagrinejamos eliptinio tipo lygtys su mišriomis išvestinemis. Šioms diferencialinems lygtims pasiūlytos naujos antros eiles baigtiniu skirtumu schemos, kurios yra monotoniškos ir konservatyvios. Sukonstruoti algoritmai tenkina skaitini maksimumo principa, kai koeficientai prie mišriuju išvestiniu gali būti bet kokio ženklo. Gauti aprioriniai iverčiai maksimumo normoje. Irodyta baigtiniu skirtumu schemu stabilumas ir konvergavimas.


First Published Online: 14 Oct 2010

Keyword : monotone difference scheme, conservative difference scheme, elliptic equations, mixed derivatives, grid maximum principle

How to Cite
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
Published in Issue
Jun 30, 2004
Abstract Views
245
PDF Downloads
87