A representation formula for linear volterra integral equations

J. M. Bownds; J. M. Cushing

doi:10.1090/S0002-9904-1973-13189-1

A representation formula for linear volterra integral equations

J. M. Bownds
, J. M. Cushing

Mathematics

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

8 Scopus citations

Abstract

It is shown that the solution to a finite system of linear Volterra integral equations may be expressed in terms of the fundamental solution to a so-called associated system of ordinary differential equations. The only requirement on the kernel is that it be expandable in a sufficiently convergent series of continuous matrices.

Original language	English (US)
Pages (from-to)	532-536
Number of pages	5
Journal	Bulletin of the American Mathematical Society
Volume	79
Issue number	3
DOIs	https://doi.org/10.1090/S0002-9904-1973-13189-1
State	Published - May 1973

Keywords

Infinite systems of ordinary differential equations
Representation formulas
Volterra integral equations

ASJC Scopus subject areas

General Mathematics
Applied Mathematics

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10.1090/S0002-9904-1973-13189-1

Cite this

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abstract = "It is shown that the solution to a finite system of linear Volterra integral equations may be expressed in terms of the fundamental solution to a so-called associated system of ordinary differential equations. The only requirement on the kernel is that it be expandable in a sufficiently convergent series of continuous matrices.",

keywords = "Infinite systems of ordinary differential equations, Representation formulas, Volterra integral equations",

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year = "1973",

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AU - Cushing, J. M.

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AB - It is shown that the solution to a finite system of linear Volterra integral equations may be expressed in terms of the fundamental solution to a so-called associated system of ordinary differential equations. The only requirement on the kernel is that it be expandable in a sufficiently convergent series of continuous matrices.

KW - Infinite systems of ordinary differential equations

KW - Representation formulas

KW - Volterra integral equations

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A representation formula for linear volterra integral equations

Abstract

Keywords

ASJC Scopus subject areas

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