Geodesic
A rate of convergence and error estimates for difference methods used to approximate solutions to ill-posed Cauchy problems in a Banach space
Numerical methods and programming, Tome 7 (2006) no. 2, pp. 163-171

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A class of finite difference methods of solving ill-posed Cauchy problems for abstract linear differential equations with sectorial operators in a Banach space is studied. Under various a priori assumptions on a solution, we establish several time-uniform estimates for the accuracy of finite difference approximations. We also give some estimates for errors caused by perturbations of initial conditions.
Keywords: sectorial operators, differential equations, ill- posed problems, finite difference methods, error estimates.
Mots-clés : conditions of sourcewise representation 
@article{VMP_2006_7_2_a0,
     author = {A. B. Bakushinskii and M. Yu. Kokurin and V. V. Klyuchev},
     title = {A rate of convergence and error estimates for difference methods used to approximate solutions to ill-posed {Cauchy} problems in a {Banach} space},
     journal = {Numerical methods and programming},
     pages = {163--171},
     publisher = {mathdoc},
     volume = {7},
     number = {2},
     year = {2006},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMP_2006_7_2_a0/}
}
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A. B. Bakushinskii; M. Yu. Kokurin; V. V. Klyuchev. A rate of convergence and error estimates for difference methods used to approximate solutions to ill-posed Cauchy problems in a Banach space. Numerical methods and programming, Tome 7 (2006) no. 2, pp. 163-171. http://geodesic.mathdoc.fr/item/VMP_2006_7_2_a0/