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

This article investigates the projection-difference method for a Cauchy problem for a linear operator-differential equation with a leading self-adjoint operator A(t) and a subordinate linear operator K(t) in Hilbert space. This method leads to the solution of a system of linear algebraic equations on each time level; moreover, the projection subspaces are linear spans of eigenvectors of an operator similar to A(t). The convergence estimates are obtained. The application of the developed method for solving the initial boundary value problem is given.