Error estimates for a projection-difference method for a linear differential-operator equation (Q731572)

The author studies a projection-difference method for the Cauchy problem \[ u^{\prime}(t)+A(t)u(t)+K(t)u(t)=h(t), \quad u(0)=0 \] with a principal self-adjoint operator coefficient \(A(t)\) and a subordinate linear operator \(K(t)\) with \(t\) - independent domains in a Hilbert space. The discretization in \(t\) is based on a three-level difference scheme. The resulting operator equation on each \(t\)-level is discretized by the Galerkin method with the appropriate chosen basic elements. An error estimate is given.