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Journal of Scientific Computing
Published in: Journal of Scientific Computing 1/2017

15-09-2016

A Collocation Boundary Value Method for Linear Volterra Integral Equations

Authors: Junjie Ma, Shuhuang Xiang

Published in: Journal of Scientific Computing | Issue 1/2017

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Abstract

This paper is devoted to studying the boundary value method for Volterra integral equations. High order numerical schemes are devised by using special multistep collocation methods, which depend on numerical approximations of the solution in the next several steps. Stability analysis illustrates these methods enjoy wide absolutely stable regions. With the help of efficient evaluation for highly oscillatory integrals, these methods are applied to solving Volterra integral equations with highly oscillatory kernels. Both theoretical and numerical results show they share the property that the higher the oscillation, the better the accuracy of the approximations.
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Footnotes
1
In the remaining part, we will abbreviate \(F_n(t_{n,i})\) to [Lag Term] for simplicity.
 
2
To make use of the same collocation grid as CBVM, the stepsize of CCM is chosen to be 2h.
 
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Metadata
Title
A Collocation Boundary Value Method for Linear Volterra Integral Equations
Authors
Junjie Ma
Shuhuang Xiang
Publication date
15-09-2016
Publisher
Springer US
Published in
Journal of Scientific Computing / Issue 1/2017
Print ISSN: 0885-7474
Electronic ISSN: 1573-7691
DOI
https://doi.org/10.1007/s10915-016-0289-3

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