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Stability and Regularization of Three-Level Difference Schemes with Unbounded Operator Coefficients in Banach Spaces
SIAM Journal on Numerical Analysis
A bstract. The problem of stability of difference schemes for second-order evolution problems is considered. Difference schemes are treated as abstract Cauchy problems for difference equations with operator coefficients in a Banach or Hilbert space. To construct stable difference schemes the regularization principle is employed, i.e., one starts from any simple scheme (possibly unstable) and derives absolutely stable schemes by perturbing the operator coefficients. The main result of this paperdoi:10.1137/s0036142999357221 fatcat:zsrargrvmzcbxl5ivp6fnldeji