Projection-difference method for a linear operator-differential equation

Asymptotic estimates of a projection-difference method for an operator-differential equation

“…However, in applications it is not always possible to find the explicit form of eigenvectors. In this paper, with the help of the moments method the approximate solution of the Cauchy problem for linear operator-differential equation is constructed in separable Hilbert space H. In contrast to [16] and [18] here the basis elements are not eigenvectors of a similar operator, which significantly expands the class of problems. In [18] a leading operator A and similar operator B satisfy the acute-angle inequality and a subordinate operator K is independent on the time variable.…”

“…Stability and convergence of various difference schemes for nonstationary operator equations were studied in [8,9,13]. Full discretization for linear differential-operator equations based on Galerkin method was carried out in [16,18], where eigenvectors of the operator similar to the leading operator A of the equation were used as the basis functions. However, in applications it is not always possible to find the explicit form of eigenvectors.…”