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A Collocation Boundary Value Method for Linear Volterra Integral Equations

Zeitschrift:: Journal of Scientific Computing > Ausgabe 1/2017

Autoren:: Junjie Ma, Shuhuang Xiang

Wichtige Hinweise

This work is supported by No.11371376 of NSF of China, the Innovation-Driven Project and the Mathematics and Interdisciplinary Sciences Project of Central South University.

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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Titel: A Collocation Boundary Value Method for Linear Volterra Integral Equations
Autoren:: Junjie Ma
Shuhuang Xiang
Publikationsdatum: 15.09.2016
DOI: https://doi.org/10.1007/s10915-016-0289-3
Verlag: Springer US
Zeitschrift: Journal of Scientific Computing
Ausgabe 1/2017
Print ISSN: 0885-7474
Elektronische ISSN: 1573-7691

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