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
Authors who publish with this journal agree to the following terms
that this article contains no violation of any existing copyright or other third party right or any material of a libelous, confidential, or otherwise unlawful nature, and that I will indemnify and keep indemnified the Editor and THE PUBLISHER against all claims and expenses (including legal costs and expenses) arising from any breach of this warranty and the other warranties on my behalf in this agreement;
that I have obtained permission for and acknowledged the source of any illustrations, diagrams or other material included in the article of which I am not the copyright owner.
on behalf of any co-authors, I agree to this work being published in the above named journal, Open Access, and licenced under a Creative Commons Licence, 4.0 https://creativecommons.org/licenses/by/4.0/legalcode. This licence allows for the fullest distribution and re-use of the work for the benefit of scholarly information.
For authors that are not copyright owners in the work (for example government employees), please contact VILNIUS TECHto make alternative agreements.
