Geodesic
Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed Cauchy problems of the second order
Numerical methods and programming, Tome 18 (2017) no. 4, pp. 322-347.

Voir la notice de l'article provenant de la source Math-Net.Ru

Finite-difference schemes of solving ill-posed Cauchy problems for linear second-order differential operator equations in Banach spaces are considered. Several time-uniform 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 second-order ill-posed Cauchy problems are proposed on the basis of combining the half-discretization in time with the discrete approximation of the spaces and the operators.
Keywords: ill-posed Cauchy problem, Banach space, finite-difference scheme, rate of convergence, error estimate, operator calculus, sectorial operator, finite-dimensional approximation.
Mots-clés : interpolation of Banach spaces 
@article{VMP_2017_18_4_a0,
     author = {M. M. Kokurin},
     title = {Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed {Cauchy} problems of the second order},
     journal = {Numerical methods and programming},
     pages = {322--347},
     publisher = {mathdoc},
     volume = {18},
     number = {4},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a0/}
}
TY  - JOUR
AU  - M. M. Kokurin
TI  - Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed Cauchy problems of the second order
JO  - Numerical methods and programming
PY  - 2017
SP  - 322
EP  - 347
VL  - 18
IS  - 4
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a0/
LA  - ru
ID  - VMP_2017_18_4_a0
ER  - 
%0 Journal Article
%A M. M. Kokurin
%T Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed Cauchy problems of the second order
%J Numerical methods and programming
%D 2017
%P 322-347
%V 18
%N 4
%I mathdoc
%U http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a0/
%G ru
%F VMP_2017_18_4_a0
M. M. Kokurin. Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed Cauchy problems of the second order. Numerical methods and programming, Tome 18 (2017) no. 4, pp. 322-347. http://geodesic.mathdoc.fr/item/VMP_2017_18_4_a0/