We consider a linear finite-difference problem in real time on a region composed of two subdomains, one of which contains the source terms that excite the solution. The deviation of solution from zero on the other subdomain is interpreted as undesirable noise. We derive the auxiliary sources (i.e., controls) that reduce this noise by a given factor . The idea of keeping a weak noise on the protected subdomain facilitates the construction of noise-suppressing active controls in real time, using only the information about the controlled process that is available up to the current moment of time near the interface between the two subdomains.

Mathematical problems and theory of numerical methods