DOI: https://doi.org/10.26089/NumMet.v18r428

Rate of convergence and error estimates for finite-difference schemes of solving linear ill-posed Cauchy problems of the second order

Authors

  • M.M. Kokurin

Keywords:

ill-posed Cauchy problem
Banach space
finite-difference scheme
rate of convergence
error estimate
operator calculus
sectorial operator
interpolation of Banach spaces
finite-dimensional approximation

Abstract

Finite-difference schemes of solving ill-posed Cauchy problems for linear second-order differential operator equations in Banach spaces are considered. Several time-uniform rate of convergence and error estimates are obtained for the considered schemes under the assumption that the sought solution satisfies the sourcewise condition. Necessary and sufficient conditions are found in terms of sourcewise index for a class of schemes with the power convergence rate with respect to the discretization step. A number of full discretization schemes for second-order ill-posed Cauchy problems are proposed on the basis of combining the half-discretization in time with the discrete approximation of the spaces and the operators.

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Published

2017-08-21

Issue

Vol. 18 (2017): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

M.M. Kokurin

Mari State University,
The Faculty of Physics and Mathematics
• Lecturer

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