05.13.18 (Mathematical modeling, numerical methods, and the program systems)
E-mail:
Keywords:
variational principles; mixed numerical methods; the theory of approximation; orthogonal compactly supported functions; wavelets.
Subject:
The new techniques of construction of orthogonal compactly supported functions are developed, which have the certain advantages before wavelets. The variational grid methods connected to mixed variational principles and to such orthogonal compactly supported functions are investigated.
Biography
Graduated from Faculty of Physics and Mechanics of the Leningrad Polytechnical Institute in 1973 (department of mechanics and control processes).
Main publications:
Leontev V. L., Lukashanets N. Ch. O setochnykh bazisakh ortogonalnykh finitnykh funktsii // Zhurnal vychislit. matematiki i matem. fiziki, 1999, t. 39, # 7, 1158–1168.
Leontev V. L. Ortogonalnye finitnye funktsii v zadachakh na sobstvennye znacheniya // Zhurnal vychislit. matematiki i matem. fiziki, 2001, t. 41, # 6, 874–880.
V. L. Leontiev, “Fourier method related with orthogonal splines in parabolic initial boundary value problem for domain with curvilinear boundary”, Ufimsk. Mat. Zh., 14:2 (2022), 58–69; Ufa Math. J., 14:2 (2022), 56–66
2.
V. L. Leont'ev, “Finite Fourier series in hyperbolic initial-boundary value problems for domains with curved boundaries”, Zh. Vychisl. Mat. Mat. Fiz., 62:10 (2022), 1662–1681; Comput. Math. Math. Phys., 62:10 (2022), 1632–1650
2017
3.
S. V. Bulyarskii, A. A. Dudin, A. P. Orlov, A. A. Pavlov, V. L. Leontev, “Forced vibration of a carbon nanotube with emission currents in an electromagnetic field”, Zhurnal Tekhnicheskoi Fiziki, 87:11 (2017), 1624–1627; Tech. Phys., 62:11 (2017), 1627–1630
A. V. Shchurenko, V. L. Leontiev, “Compactly supported functions in cryptography algorithms”, Prikl. Diskr. Mat., 2017, no. 36, 73–83
2015
5.
V. L. Leontiev, “Orthogonal Franklin system and orthogonal system of finite functions in numerical methods of boundary problems solving”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 19:2 (2015), 398–404
2011
6.
V. L. Leont'ev, A. V. Kochulimov, “On orthogonal second order finite functions associated with triangular meshes and their application in mathematical modeling”, Vestn. Samar. Gos. Tekhn. Univ., Ser. Fiz.-Mat. Nauki [J. Samara State Tech. Univ., Ser. Phys. Math. Sci.], 1(22) (2011), 241–243
2009
7.
V. L. Leont'ev, “О численном методе решения задач теории пластичности”, Matem. Mod. Kraev. Zadachi, 1 (2009), 145–146
2008
8.
A. V. Kochulimov, V. L. Leont'ev, “Orthogonal finite functions of the second degree on triangular meshes and their application in geometrical models”, Trudy SVMO, 10:2 (2008), 126–129
2006
9.
V. L. Leont'ev, E. A. Rikov, “Integral transforms associated with orthogonal finite functions in the spectral analysis of signals”, Matem. Mod., 18:7 (2006), 93–100
V. L. Leont'ev, E. A. Rikov, “Интегральные ОФФ преобразования в задачах моделирования сигналов”, Matem. Mod. Kraev. Zadachi, 2 (2005), 168–170
12.
A. R. Krasilnikov, V. L. Leont'ev, “Апостериорная оценка точности приближенного решения краевой задачи изгиба пластины”, Matem. Mod. Kraev. Zadachi, 1 (2005), 157–160
2004
13.
V. L. Leont'ev, “Об ортогональных финитных функциях и связанных с ними вариационно-сеточных методах решения краевых задач”, Matem. Mod. Kraev. Zadachi, 3 (2004), 140–143
2003
14.
V. L. Leont'ev, A. Yu. Melent'ev, “Grid methods of calculations curvilinear bars”, Matem. Mod., 15:10 (2003), 95–104
2002
15.
V. L. Leont'ev, “Orthogonal splines and variational-grid method”, Matem. Mod., 14:3 (2002), 117–127
V. L. Leont'ev, A. Yu. Melent'ev, “Orthogonal finite functions in variational-grid methods of the theory of curvilinear bars”, Matem. Mod., 14:2 (2002), 39–50
V. L. Leont'ev, “About convergence of a mixed variational-grid method”, Sib. Zh. Vychisl. Mat., 5:1 (2002), 25–34
2001
18.
V. L. Leont'ev, N. Ch. Lukashanets, “Orthogonal compactly supported functions on triangular grids and their use in a mixed variational-difference method”, Zh. Vychisl. Mat. Mat. Fiz., 41:7 (2001), 1090–1098; Comput. Math. Math. Phys., 41:7 (2001), 1038–1046
19.
V. L. Leont'ev, “Orthogonal compactly supported functions in eigenvalue problems”, Zh. Vychisl. Mat. Mat. Fiz., 41:6 (2001), 874–880; Comput. Math. Math. Phys., 41:6 (2001), 825–831