Boundedness of solutions of difference equations and application to numerical solution of Volterra integral equations of the second kind

V. L. Bakke, Z. Jackiewicz

Research output: Contribution to journalArticlepeer-review

6 Scopus citations

Abstract

We study the difference equations obtained when some numerical methods for Volterra integral equations of the second kind are applied to the linear test problem y(t) = 1 + ∝0t (λ + μt + vs) y(s) ds, t ≥ 0, with fixed stepsize h. The resulting difference equations are of Poincaré type and we formulate a criterion for boundedness of solutions of these equations if the associated characteristic polynomial is a simple von Neumann polynomial. This result is then used in stability analysis of reducible quadrature methods for Volterra integral equations.

Original languageEnglish (US)
Pages (from-to)592-605
Number of pages14
JournalJournal of Mathematical Analysis and Applications
Volume115
Issue number2
DOIs
StatePublished - May 1 1986
Externally publishedYes

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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