Abstract:
In this paper we obtain an a priori estimate for solution of Tricomi problem for the Lavrent'ev–Bitsadze equation, from which the uniqueness of regular solution follows. Presented a numerical finite-difference method for solving the investigated problem. We obtain an a priori estimate for solution of the difference scheme, from which follows the second-order convergence.
Keywords:
equation of mixed type, Tricomi problem, a priori estimate, difference scheme, order of approximation, method of energy inequalities.
Citation:
Zh. A. Balkizov, A. A. Sokurov, “Finite-difference method for solving Tricomi problem for the Lavrent'ev–Bitsadze equation”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 21:2 (2017), 221–235
\Bibitem{BalSok17}
\by Zh.~A.~Balkizov, A.~A.~Sokurov
\paper Finite-difference method for solving Tricomi problem for the Lavrent'ev--Bitsadze equation
\jour Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.]
\yr 2017
\vol 21
\issue 2
\pages 221--235
\mathnet{http://mi.mathnet.ru/vsgtu1534}
\crossref{https://doi.org/10.14498/vsgtu1534}
\zmath{https://zbmath.org/?q=an:06964670}
\elib{https://elibrary.ru/item.asp?id=30039925}
Linking options:
https://www.mathnet.ru/eng/vsgtu1534
https://www.mathnet.ru/eng/vsgtu/v221/i2/p221
This publication is cited in the following 2 articles:
G. A. Balkizov, “On a Priori Estimates of Solutions of the Tricomi Problem for a Certain Mixed-Type Second-Order Equation”, J Math Sci, 260:3 (2022), 286
Zh. A. Balkizov, “Ob apriornoi otsenke resheniya zadachi Trikomi dlya odnogo uravneniya smeshannogo tipa vtorogo poryadka”, Materialy IV Mezhdunarodnoi nauchnoi konferentsii “Aktualnye problemy prikladnoi matematiki”. Kabardino-Balkarskaya respublika, Nalchik, Prielbruse, 22–26 maya 2018 g. Chast III, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 167, VINITI RAN, M., 2019, 14–20
Citation in format AMSBIB
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