DOI: https://doi.org/10.26089/NumMet.v19r438

On some properties of the projection operator for a class of stabilization algorithms

Authors

  • A.A. Kornev

Keywords:

numerical methods
projection operator
stabilization

Abstract

The projection operator Q[a] acting from the linear space of the functions a(x) ∈ span{sin ix, i ≥ 1} given on the segment [0,π] onto the subspace of the functions ã(x) ∈ span{sin ix, i > i0} is studied theoretically and numerically. The corresponding projection is performed along the subspace of the functions l(x) ∈ span{sin ix, i=1,...,i0}, where sin ix = χ δ(x)sin ix, χ δ(x) is the characteristic function χ δ(x) of the interval [0,δ]. The obtained results are used to solve the problem of stabilization with respect to the initial data of solutions to the model nonstationary equations.

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Published

2018-12-24

Issue

Vol. 19 (2018): Issue 4.

Section

Section 1. Numerical methods and applications

Author Biography

A.A. Kornev

Lomonosov Moscow State University,
Faculty of Mechanics and Mathematics
• Professor

References

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