A stability analysis of the trapezoidal method for Volterra integral equations with completely positive kernels

A. Bellen, Zdzislaw Jackiewicz, R. Vermiglio, M. Zennaro

Research output: Contribution to journalArticle

4 Scopus citations

Abstract

The solution of the Volterra integral equation with completely positive kernel y(t) + ∝0t b(t - s) y(s) ds = u0 + ∝0t b(t - s) g(s) ds, t ≥ 0, is nonnegative and nonincreasing provided that g is nonincreasing and 0 ≤ g(t) ≤ u0 for any t > 0. We prove that under some additional hypotheses this property is inherited by the solution of the recurrence relation resulting from applying the trapezoidal method to this equation.

Original languageEnglish (US)
Pages (from-to)324-342
Number of pages19
JournalJournal of Mathematical Analysis and Applications
Volume152
Issue number2
DOIs
StatePublished - Nov 1 1990

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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