On a complete discretization scheme for an ill-posed Cauchy problem in a Banach space

被引：2
|
作者：
Bakushinskii, A. B. [1 ]
Kokurin, M. M. [2 ]
Kokurin, M. Yu [2 ]
机构：
[1] Russian Acad Sci, Inst Syst Anal, Moscow 117312, Russia
[2] Mari State Univ, Yoshkar Ola 424001, Russia
来源：
PROCEEDINGS OF THE STEKLOV INSTITUTE OF MATHEMATICS | 2013年 / 280卷
基金：
俄罗斯基础研究基金会;
关键词：
Cauchy problem; ill-posed problem; discretization; regularization; error estimate;
D O I：
10.1134/S0081543813020053
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
A complete discretization scheme for an ill-posed Cauchy problem for abstract firstorder linear differential equations with sectorial operators in a Banach space is validated. The scheme combines a time semidiscretization of the equations and a finite-dimensional approximation of the spaces and operators. Regularization properties of the scheme are established. Error estimates are obtained in the case of approximate initial data under various a priori assumptions concerning the solution.
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页码：53 / 65
页数：13
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