On mixed collocation methods for Volterra integral equations with periodic solution

H. Brunner; Athena Makroglou; R. K. Miller

doi:10.1016/S0168-9274(97)00015-9

On mixed collocation methods for Volterra integral equations with periodic solution

H. Brunner
, Athena Makroglou
, R. K. Miller

Research output: Contribution to journal › Article › peer-review

Abstract

In this paper we extend recent results for the numerical solution of Volterra integro-differential equations with periodic solution (Brunner, Makroglou and Miller, 1996) to the numerical solution of Volterra integral equations with periodic solution. We apply collocation and iterated collocation methods based on the mixed interpolation methods of De Meyer, Vanthournout and Vanden Berghe (1990). The existence of unique continuous periodic solutions is examined and a convergence analysis of the numerical method is given. Numerical results are included for comparison with the polynomial collocation methods based on Lobatto and Gauss points as collocation parameters.

Original language	English
Pages (from-to)	115-130
Journal	Applied Numerical Mathematics
Volume	24
Issue number	2-3
DOIs	https://doi.org/10.1016/S0168-9274(97)00015-9
Publication status	Published - 1 Aug 1997
Event	2nd International Conference on the Numerical Solution of Volterra and Delay Equations - Arizona State University, Arizona, USA Duration: 27 May 1996 → 30 May 1996

Keywords

numerical solution
Volterra integral equation
periodic
mixed interpolation
collocation

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10.1016/S0168-9274(97)00015-9

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title = "On mixed collocation methods for Volterra integral equations with periodic solution",

abstract = "In this paper we extend recent results for the numerical solution of Volterra integro-differential equations with periodic solution (Brunner, Makroglou and Miller, 1996) to the numerical solution of Volterra integral equations with periodic solution. We apply collocation and iterated collocation methods based on the mixed interpolation methods of De Meyer, Vanthournout and Vanden Berghe (1990). The existence of unique continuous periodic solutions is examined and a convergence analysis of the numerical method is given. Numerical results are included for comparison with the polynomial collocation methods based on Lobatto and Gauss points as collocation parameters.",

keywords = "numerical solution, Volterra integral equation, periodic, mixed interpolation, collocation",

author = "H. Brunner and Athena Makroglou and Miller, \{R. K.\}",

year = "1997",

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doi = "10.1016/S0168-9274(97)00015-9",

language = "English",

volume = "24",

pages = "115--130",

journal = "Applied Numerical Mathematics",

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note = "2nd International Conference on the Numerical Solution of Volterra and Delay Equations ; Conference date: 27-05-1996 Through 30-05-1996",

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TY - JOUR

T1 - On mixed collocation methods for Volterra integral equations with periodic solution

AU - Brunner, H.

AU - Makroglou, Athena

AU - Miller, R. K.

PY - 1997/8/1

Y1 - 1997/8/1

N2 - In this paper we extend recent results for the numerical solution of Volterra integro-differential equations with periodic solution (Brunner, Makroglou and Miller, 1996) to the numerical solution of Volterra integral equations with periodic solution. We apply collocation and iterated collocation methods based on the mixed interpolation methods of De Meyer, Vanthournout and Vanden Berghe (1990). The existence of unique continuous periodic solutions is examined and a convergence analysis of the numerical method is given. Numerical results are included for comparison with the polynomial collocation methods based on Lobatto and Gauss points as collocation parameters.

AB - In this paper we extend recent results for the numerical solution of Volterra integro-differential equations with periodic solution (Brunner, Makroglou and Miller, 1996) to the numerical solution of Volterra integral equations with periodic solution. We apply collocation and iterated collocation methods based on the mixed interpolation methods of De Meyer, Vanthournout and Vanden Berghe (1990). The existence of unique continuous periodic solutions is examined and a convergence analysis of the numerical method is given. Numerical results are included for comparison with the polynomial collocation methods based on Lobatto and Gauss points as collocation parameters.

KW - numerical solution

KW - Volterra integral equation

KW - periodic

KW - mixed interpolation

KW - collocation

U2 - 10.1016/S0168-9274(97)00015-9

DO - 10.1016/S0168-9274(97)00015-9

M3 - Article

VL - 24

SP - 115

EP - 130

JO - Applied Numerical Mathematics

JF - Applied Numerical Mathematics

IS - 2-3

T2 - 2nd International Conference on the Numerical Solution of Volterra and Delay Equations

Y2 - 27 May 1996 through 30 May 1996

ER -

On mixed collocation methods for Volterra integral equations with periodic solution

Abstract

Keywords

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