Stability and regularization of three-level difference schemes with unbounded operator coefficients in Banach spaces (Q2719231)

The problem of stability of difference schemes for second-order evolution equations is considered. The difference schemes are treated as abstract Cauchy problems for difference equations with operator coefficients in a Banach or Hilbert space. The regularization principle is employed to construct stable difference schemes. It starts from any simple scheme and derives absolutely stable schemes by perturbing the operator coefficients.NEWLINENEWLINENEWLINEThe aim of this paper is to obtain stability results for regularized three-level difference schemes with unbounded operator coefficients in a Banach space. For example this class of schemes arises when approximating second-order evolution differential equations.