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

V. L. Bakke, Zdzislaw Jackiewicz

Research output: Contribution to journalArticle

6 Citations (Scopus)

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 + ∝0 t (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

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Boundedness of Solutions
Volterra Integral Equations
Difference equations
Difference equation
Integral equations
Polynomials
Numerical Solution
Quadrature Method
Associated Polynomials
Characteristic polynomial
Test Problems
Stability Analysis
Numerical methods
Numerical Methods
Polynomial

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

Cite this

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AB - 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 + ∝0 t (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.

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