On stability of difference schemes in fractional spaces

Abstract

a b s t r a c tThe Cauchy problem 0)) and with an arbitrary ε positive parameter multiplying the derivative term is considered. The first order of accuracy single-step uniform difference scheme for the solution of this problem is presented. The stability and convergence estimates for the solution of this difference scheme in fractional spaces are obtained. The theorem on the well-posedness of this difference scheme in fractional spaces is established. Convergence estimates for the solution of the Cauchy problem for multi-dimensional parabolic equations with an arbitrary ε positive parameter multiplying the derivative term are obtained.