My scientific interests are in the field of numerical methods for solving differential and integral equations, in particular - the methods of finite differences, finite elements, boundary elements, as well as their application to the mathematical models of physical and industrial processes.
Differential Equations, Dynamical Systems, Mathematical Physics.
My mathematical work is primary connected with the approximation theory. Other areas of interest are varying fields of analysis, analytic number theory, numerical methods and mathematical modeling. I am also interested in the theory and application of the electoral systems, election conduct and observation.
I carry out research mostly in the field of approximation theory. In the recent years I have been particularly interested in establishing a precise and useful characterization of the rate of convergence of various approximation processes generated either by linear operators or by non-linear as best (weighted) approximation by algebraic or trigonometric polynomials. My research also includes interpolation, (generalized) Fourier expansions, orthogonal polynomials, quadrature formulae, multipliers, application of Fourier analysis in approximation theory, and functional analysis.
Numerical methods for nonlinear partial differential equations – finite element and finite difference methods; algorithms and scientific software; Numerical analysis of nonlinear and spectral problems in hydrodynamics, quantum mechanics, nonlinear heat - conducting medium; Numerical investigation of solutions to generalized Boussinesq’s type equations; Global solvability or finite time blow up of Cauchy problem for generalized Boussinesq’s type equations.
Dynamical systems, Applications in mathematical modeling of bioprocesses, Computer-oriented numerical analysis.
Numerical methods; Approximation theory; Spline-functions; Interpolation and approximation by radon projection data; Aproximating harmonic functions through Radon projections; Low rank approximations.
Numerical solution of partial differential equations, Finite elements, Multilevel methods.
Mathematical modeling of biological processes, Bifurcation analysis of dynamical system, Computer simulations of biological models
Mathematical modeling and computer simulation of multiphase flows with heat and mass transfer and bioprocesses.
