Approximate open boundary conditions for a class of hyperbolic equations

Initial-boundary value problems formulated in spatially unbounded domains can be sometimes reduced to problems in their bounded subdomains by using the so-called open boundary conditions. These conditions are set on the surface separating the subdomain from the rest of the domain. One of the approaches to obtaining such a kind of conditions is based on an approximation of the kernels of the time convolution operators in the relations connecting the exact solution of the original problem and its derivatives on the open boundary. In this case, it is possible to considerably reduce the requirements for system resources required to solve numerically for a wide range of physical and engineering problems. Estimates of the perturbations of the exact solution due to the approximate conditions are obtained for a model problem with one space variable.