Employment of a Small Parameter in Construction of Artificial Boundary Conditions by Means of Difference Potentials Method

A difference problem which decision we are interested in only into certain grid subdomain is considered on a finite grid. Outside of this subdomain the problem is described by linear equations with constant coefficients. Due to difference potentials method we can deal with nonlocal conditions written on the artificial grid boundary of the computational subdomain instead of the above mentioned linear equations. Under some assumptions the introduction of a small parameter to the auxiliary problem allows to construct the approximate artificial boundary conditions using the auxiliary problem convenient for computations. The matrix of the obtained approximate conditions converges to the matrix of the precise artificial boundary conditions if the parameter tends to zero. The estimation of the convergence is obtained.