Research interests 

Theory of stability and correctness of operator-difference schemes 

• Conditions for stability of two-and three-level operator-difference schemes with nonselfadjoint operators 

• A strong (coefficient) stability operator-difference schemes 

• SM-stability of operator-difference schemes 

Additive operator-difference scheme (splitting scheme) 

• Vector additive scheme (scheme of  multicomponent splitting) 

• Regularized additive schemes with 8full approximation 

• Additive schemes for system of unsteady equations 

Domain decomposition method for nonstationary problems of mathematical physics 

• Regionally additive scheme of multicomponent splitting 

• Domain decomposition method for systems of evolution equations 

• Parallel domain decomposition algorithms for problems of mathematical physics 

Numerical methods for solving inverse problems of mathematical physics 

• The stability of operator-difference schemes for ill-posed evolution problems 

• Regularized difference schemes 

• Identification problems of the coefficients and right hand sides of the equations of mathematical physics 

Applied Problems 

• Problems of hydrodynamics of an incompressible fluid 

• Numerical methods for solving poroelastic problems

• Simulation of physical processes in aluminum reduction cell