### 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 language | English (US) |
---|---|

Pages (from-to) | 592-605 |

Number of pages | 14 |

Journal | Journal of Mathematical Analysis and Applications |

Volume | 115 |

Issue number | 2 |

DOIs | |

State | Published - May 1 1986 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Analysis
- Applied Mathematics

### Cite this

**Boundedness of solutions of difference equations and application to numerical solution of Volterra integral equations of the second kind.** / Bakke, V. L.; Jackiewicz, Zdzislaw.

Research output: Contribution to journal › Article

}

TY - JOUR

T1 - Boundedness of solutions of difference equations and application to numerical solution of Volterra integral equations of the second kind

AU - Bakke, V. L.

AU - Jackiewicz, Zdzislaw

PY - 1986/5/1

Y1 - 1986/5/1

N2 - 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.

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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UR - http://www.scopus.com/inward/citedby.url?scp=0022715556&partnerID=8YFLogxK

U2 - 10.1016/0022-247X(86)90018-1

DO - 10.1016/0022-247X(86)90018-1

M3 - Article

AN - SCOPUS:0022715556

VL - 115

SP - 592

EP - 605

JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

SN - 0022-247X

IS - 2

ER -