My research interests include theoretical proof of applying the projective-difference methods to finding an approximate solution of evolutional, to be more exact, parabolic problems. I have received accuracy estimations (in adequate norms) of the approximate solutions of parabolic problems obtained using semi-discrete Galerkin's method and projective-difference methods which include the implicit Euler's scheme, Krank–Nikolson's scheme and some of its modifications. The convergence have been established and here have been also investigated the relation between the order of the speed of error convergence to 0 and various smoothness conditions of the parabolic problem initial data and its solution.
Biography
Graduated from Faculty of Mathematics and Mechanics of Voronezh State University (VSU) in 1969 (department of functional analysis and operator equations). Ph.D. thesis was defended in 1981. D. thesis was defended in 2002. A list of my works contains more than 100 titles.
Main publications:
Smagin V. V. Otsenki pogreshnosti poludiskretnykh priblizhenii po Galerkinu dlya parabolicheskikh uravnenii s kraevym usloviem tipa Neimana // Izv. vuzov. Matematika, 1996, 3(406), 50-57.
Smagin V. V. Otsenki skorosti skhodimosti proektsionnogo i proektsionno-raznostnogo metodov dlya slabo razreshimykh parabolicheskikh uravnenii // Matemat. sbornik, 1997, 188(3), 143-160.
Smagin V.V. Srednekvadratichnye otsenki pogreshnosti proektsionno-raznostnogo metoda dlya parabolicheskikh uravnenii // Zhurn. vychislit. matem. i matem. fizika, 2000, 40(6), 908-919.
Smagin V. V. Proektsionno-raznostnye metody priblizhennogo resheniya parabolicheskikh uravnenii s nesimmetrichnymi operatorami // Differents. ur-niya, 2001, 37(1), 115-123.
Smagin V. V. Energeticheskie otsenki pogreshnosti proektsionno-raznostnogo metoda so skhemoi Kranka-Nikolson dlya parabolicheskikh uravnenii // Sibirskii matem. zh., 2001, 42(3), 670-682.
A. S. Bondarev, V. V. Smagin, “Solving a variational parabolic equation with the periodic condition by a projection-difference method with the Crank–Nicolson scheme in time”, Sibirsk. Mat. Zh., 58:4 (2017), 761–770; Siberian Math. J., 58:4 (2017), 591–599
A. A. Petrova, V. V. Smagin, “Convergence of the Galyorkin method of approximate solving of parabolic equation with weight integral condition on a solution”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 8, 49–59; Russian Math. (Iz. VUZ), 60:8 (2016), 42–51
V. V. Smagin, “On the Rate of Convergence of Projection-Difference Methods for Smoothly Solvable Parabolic Equations”, Mat. Zametki, 78:6 (2005), 907–918; Math. Notes, 78:6 (2005), 841–852
V. V. Smagin, “Strong-Norm Error Estimates for the Projective-Difference Method for Parabolic Equations with Modified Crank–Nicolson Scheme”, Mat. Zametki, 74:6 (2003), 913–923; Math. Notes, 74:6 (2003), 864–873
V. V. Smagin, “Projection-Difference Methods for the Approximate Solution of Parabolic Equations with Nonsymmetric Operators”, Differ. Uravn., 37:1 (2001), 115–123; Differ. Equ., 37:1 (2001), 128–137
V. V. Smagin, “Energy error estimates for the projection-difference method with the Crank–Nicolson scheme for parabolic equations”, Sibirsk. Mat. Zh., 42:3 (2001), 670–682; Siberian Math. J., 42:3 (2001), 568–578
V. V. Smagin, “Mean-square estimates for the error of a projection-difference method for parabolic equations”, Zh. Vychisl. Mat. Mat. Fiz., 40:6 (2000), 908–919; Comput. Math. Math. Phys., 40:6 (2000), 868–879
V. V. Smagin, “Strong-norm error estimates for the projective-difference method for approximately solving abstract parabolic equations”, Mat. Zametki, 62:6 (1997), 898–909; Math. Notes, 62:6 (1997), 752–761
V. V. Smagin, “Estimates of the rate of convergence of projective and projective-difference methods for weakly solvable parabolic equations”, Mat. Sb., 188:3 (1997), 143–160; Sb. Math., 188:3 (1997), 465–481
V. V. Smagin, “On the solvability of an abstract parabolic equation with an operator whose domain depends on time”, Differ. Uravn., 32:5 (1996), 711–712; Differ. Equ., 32:5 (1996), 723–725
V. V. Smagin, “Error estimates for semidiscrete approximations in the sense of Galerkin for parabolic equations with a Neumann-type boundary condition”, Izv. Vyssh. Uchebn. Zaved. Mat., 1996, no. 3, 50–57; Russian Math. (Iz. VUZ), 40:3 (1996), 48–55
V. V. Smagin, “Coercive error estimates for the projection-difference method for an abstract parabolic equation with an operator having time dependent domain”, Sibirsk. Mat. Zh., 37:2 (1996), 406–418; Siberian Math. J., 37:2 (1996), 350–362
V. V. Smagin, “Coercive error estimates in the projection and projection-difference methods for parabolic equations”, Mat. Sb., 185:11 (1994), 79–94; Russian Acad. Sci. Sb. Math., 83:2 (1995), 369–382
V. V. Smagin, “Convergence of semidiscrete approximations in the sense of Galerkin for quasilinear parabolic equations”, Izv. Vyssh. Uchebn. Zaved. Mat., 1989, no. 2, 62–67; Soviet Math. (Iz. VUZ), 33:2 (1989), 74–82
1979
15.
V. V. Smagin, “The rate of convergence of the Galerkin method of solution of an abstract quasilinear parabolic equation”, Differ. Uravn., 15:9 (1979), 1720–1721
1970
16.
V. V. Smagin, P. E. Sobolevskii, “Comparison theorems for the norms of the solutions of linear homogeneous differential equations in Hilbert spaces”, Differ. Uravn., 6:11 (1970), 2005–2010
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