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.
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.
