"Rate of convergence and error estimates for finitedifference schemes of
solving linear illposed Cauchy problems of the second order"
Kokurin M.M. 
Finitedifference schemes of solving illposed Cauchy problems for linear secondorder differential operator equations in Banach spaces are considered. Several timeuniform rate of convergence and error estimates are obtained for the considered schemes under the assumption that the sought solution satisfies the sourcewise condition. Necessary and sufficient conditions are found in terms of sourcewise index for a class of schemes with the power convergence rate with respect to the discretization step. A number of full discretization schemes for secondorder illposed Cauchy problems are proposed on the basis of combining the halfdiscretization in time with the discrete approximation of the spaces and the operators. Keywords: illposed Cauchy problem, Banach space, finitedifference scheme, rate of convergence, error estimate, operator calculus, sectorial operator, interpolation of Banach spaces, finitedimensional approximation.

