Geodesic
Convergence rate estimation for finite-difference methods
Numerical methods and programming, Tome 11 (2010) no. 1, pp. 25-31.

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A class of finite-difference methods for solving the ill-posed Cauchy problem for second-order linear differential equations with sectorial operators in a Banach space is studied. Several convergence rate estimates for finite-difference approximations are proposed under some prior assumptions on the solution to the Cauchy problem.
Keywords: operator differential equation; Cauchy problem; ill-posed problem; sectorial operator; finite-difference methods. 
@article{VMP_2010_11_1_a3,
     author = {A. B. Bakushinskii and M. Yu. Kokurin and V. V. Klyuchev},
     title = {Convergence rate estimation for finite-difference methods},
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     pages = {25--31},
     publisher = {mathdoc},
     volume = {11},
     number = {1},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2010_11_1_a3/}
}
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A. B. Bakushinskii; M. Yu. Kokurin; V. V. Klyuchev. Convergence rate estimation for finite-difference methods. Numerical methods and programming, Tome 11 (2010) no. 1, pp. 25-31. http://geodesic.mathdoc.fr/item/VMP_2010_11_1_a3/