"On some properties of the projection operator for a class of stabilization algorithms"
Kornev A.A.

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.

Keywords: numerical methods, projection operator, stabilization.

  • Kornev A.A. – Lomonosov Moscow State University, Faculty of Mechanics and Mathematics; Leninskie Gory, Moscow, 119899, Russia; Dr. Sci., Professor, e-mail: kornev@mech.math.msu.su