Coefficient stability of operator‐difference schemes with time variable operators

Abstract

The problem of the coefficient stability for operator‐ difference schemes with variable operator is investigated. A priori coordinated estimates in the L ₂‐norm are obtained for differential‐operator equations and operator‐difference schemes. Estimates in the energy space H_A for coefficient stability and stability with respect to the right‐hand side and the initial data are proved under more strong assumptions for operator's perturbation.

First Published Online: 14 Oct 2010