Determination of a control parameter for the difference Schrödinger equation (Q2015733)

Summary: The first order of accuracy difference scheme for the numerical solution of the boundary value problem for the differential equation with parameter \(p\), \(i(du(t)/dt)+Au(t)+iu(t)=f(t)+p\), \(0<t<T\), \(u(0)=\varphi\), \(u(T)=\psi\), in a Hilbert space \(H\) with self-adjoint positive definite operator \(A\) is constructed. The well-posedness of this difference scheme is established. The stability inequalities for the solution of difference schemes for three different types of control parameter problems for the Schrödinger equation are obtained.