Stability and absolute stability of a three-point difference scheme

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4 Scopus citations


Consider a three-point difference scheme -h-2Δ(2)yn + qn(h)yn = fn(h), n ε Z = {0, ±1, ±2,...}. where h ε (0, h0], h0 is a given positive number, Δ(2)yn = yn+1 -2yn + yn-1, f(h) = {fn(h)} n ε Z ε L(h), L(h) = {f(h) : ∥f(h)∥ L(h) < ∞}, ∥f(h)∥ L(h) = supnεZ|fn(h)|. We assume a unique a priori requirement 0 ≤ qn(h) < ∞ for any n ε Z and h ε (0, h0]. The main results are a criterion of stability and absolute stability of the difference scheme (1) in the space L(h).

Original languageEnglish
Pages (from-to)1181-1194
Number of pages14
JournalComputers and Mathematics with Applications
Issue number6-9
StatePublished - 1 Mar 2003


  • Absolute stability
  • Stability
  • Three-point difference scheme

ASJC Scopus subject areas

  • Modeling and Simulation
  • Computational Theory and Mathematics
  • Computational Mathematics


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