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

DOI10.1134/S0965542515120076zbMath1339.65071OpenAlexW2264151032MaRDI QIDQ266092

Mikhail M. Kokurin

Publication date: 13 April 2016

Published in: Computational Mathematics and Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1134/s0965542515120076

zbMATH Keywords

rate of convergenceregularizationCauchy problemfinite difference schemesill-posed problemquasi-reversibility methodabstract equation of first orderinterpolation of Banach spaces

Mathematics Subject Classification ID

Stability and convergence of numerical methods for ordinary differential equations (65L20) Linear differential equations in abstract spaces (34G10) Numerical solutions of ill-posed problems in abstract spaces; regularization (65J20) Finite difference and finite volume methods for ordinary differential equations (65L12) Numerical solutions to abstract evolution equations (65J08) Numerical solution of ill-posed problems involving ordinary differential equations (65L08)

Related Items (5)

Conditions for the qualified convergence of finite difference methods and the quasi-reversibility method for solving linear ill-posed Cauchy problems in a Hilbert space ⋮ Discrete approximation of solutions of the Cauchy problem for a linear homogeneous differential-operator equation with a Caputo fractional derivative in a Banach space ⋮ Direct and converse theorems for iterative methods of solving irregular operator equations and finite difference methods for solving ill-posed Cauchy problems ⋮ Necessary and sufficient conditions for power convergence rate of approximations in Tikhonov's scheme for solving ill-posed optimization problems ⋮ A posteriori choice of time-discretization step in finite difference methods for solving ill-posed Cauchy problems in Hilbert space

Cites Work

• On a complete discretization scheme for an ill-posed Cauchy problem in a Banach space
• The functional calculus for sectorial operators
• On sequential minimization of Tikhonov functionals in ill-posed problems with a priori information on solutions
• On a class of finite-difference schemes for solving ill-posed Cauchy problems in Banach spaces
• On error estimates of difference solution methods for ill-posed Cauchy problems in a Hilbert space
• On the eigenfunctions and on the eigenvalues of general elliptic boundary value problems
• Generation of Analytic Semigroups by Strongly Elliptic Operators Under General Boundary Conditions
• One-Parameter Semigroups for Linear Evolution Equations
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