On the numerical solution of $2m$-th elliptic problems by least squares method using splines on rectangular grids

The least squares method is proposed for numerical solution of $2m$-th – order elliptic problems with arbitrary boundary conditions. The method utilizes spline approximation on retangular grids, which are not adjusted to the shapes of the region under study. The results of investigations of 2-nd and 4-th order problems related to the elastisity theory are represented.