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

DOI10.1134/S0081543813020053zbMath1287.65041MaRDI QIDQ2446996

Mikhail Yu. Kokurin, Mikhail M. Kokurin, Anatoly B. Bakushinsky

Publication date: 23 April 2014

Published in: Proceedings of the Steklov Institute of Mathematics (Search for Journal in Brave)

zbMATH Keywords

discretizationregularizationCauchy problemerror estimateBanach spaceill-posed problemsectorial operatorstime semidiscretizationabstract first-order linear differential equations

Mathematics Subject Classification ID

Numerical methods for initial value problems involving ordinary differential equations (65L05) Error bounds for numerical methods for ordinary differential equations (65L70) Linear differential equations in abstract spaces (34G10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Numerical solutions to abstract evolution equations (65J08)

Related Items

Necessary and sufficient conditions for the polynomial convergence of the quasi-reversibility and finite-difference methods for an ill-posed Cauchy problem with exact data ⋮ Convergence of a class of Schrödinger equations ⋮ Direct and converse theorems for iterative methods of solving irregular operator equations and finite difference methods for solving ill-posed Cauchy problems ⋮ Maximal estimates for the Schrödinger equation with orthonormal initial data ⋮ A note on pointwise convergence for the Schrödinger equation

Cites Work

• On a class of finite difference methods for ill-posed Cauchy problems with noisy data
• On error estimates of difference solution methods for ill-posed Cauchy problems in a Hilbert space
• ESTIMATES OF THE RATE OF CONVERGENCE IN SOLVING ILL-POSED PROBLEMS FOR EVOLUTION EQUATIONS