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.