Regularity of the inversion problem for the Sturm-Liouville difference equation IV. Stability conditions for a three-point difference scheme with non-negative coefficients

N. A. Chernyavskaya, J. Schiff, L. A. Shuster

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Consider a three-point difference scheme -h-2Δ (2)yn + qn(h)yn = fn(h), n ∈ Z = {0, ± 1, ± 2,...} (1) where h ∈ (0, h 0], h0 is a given positive number, Δ (2)yn = yn+1 - 2yn + y n-1, f(h) =def {fn(h)}n∈Z ∈ L p(h),p ∈ [1, ∞), Lp(h) = { f(h): ∥ f (h) ∥ Lp(h) < ∞}, ∥f(h)∥|pL p(h) =∑n∈|f n(h)|p h. Assume that the sequence q(h) =def {qn(h)}n∈Z satisfies the a priori condition 0 ≤ qn(h) < ∞ ∀n ∈ Z, ∀h ∈ (0, h0]. We obtain criteria for the stability of scheme (1) in Lp(h), p ∈ [1, ∞).

Original languageEnglish
Pages (from-to)487-501
Number of pages15
JournalJournal of Difference Equations and Applications
Volume11
Issue number6
DOIs
StatePublished - 1 May 2005

Keywords

  • Difference scheme
  • Inversion problem
  • Non-negative coefficients
  • Sturm-Liouville equation

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