On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations-Reference-Cited by-同舟云学术

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On the convergence of collocation solutions in continuous piecewise polynomial spaces for Volterra integral equations

Published:2016-02-12 Issue:4 Volume:56 Page:1339-1367
ISSN:0006-3835
Container-title:BIT Numerical Mathematics
language:en
Short-container-title:Bit Numer Math

Author:

Liang Hui,Brunner Hermann

Funder

the National Nature Science Foundation of China

the Research Fund of the Heilongjiang Provincial Education Department for the Academic Backbone of the Excellent Young People

Science and Technology Innovation Team in Higher Education Institutions of Heilongjiang Province

the Heilongjiang University Science Funds for Distinguished Young Scholars

the Natural Science Foundation of Heilongjiang Province

the Hong Kong Research Grants Council

the Natural Sciences and Engineering Research Council of Canada

Publisher

Springer Science and Business Media LLC

Subject

Applied Mathematics,Computational Mathematics,Computer Networks and Communications,Software

Link

http://link.springer.com/content/pdf/10.1007/s10543-016-0609-x.pdf

Reference8 articles.

1. Brunner, H.: The use of splines in the numerical solution of differential and Volterra integral equations. In: Dubuc, S., Deslauriers, G. (eds.) Spline Functions and the Theory of Wavelets (Montreal 1996), CRM Proceedings and Lecture Notes, vol. 18, pp. 15–31. American Mathematical Society, Providence (1999)

2. Brunner, H.: Collocation Methods for Volterra Integral and Related Functional Differential Equations. Cambridge University Press, Cambridge (2004)

3. Brunner, H.: On the divergence of collocation solutions in smooth piecewise polynomial spaces for Volterra integral equations. BIT 44, 631–650 (2004)

4. El Tom, M.E.A.: On the numerical stability of spline function approximations to the solutions of Volterra integral equations of the second kind. BIT 14, 136–143 (1974)

5. Hairer, E., Lubich, Ch., N $$\phi $$ ϕ rsett, S.P.: Order of convergence of cne-step methods for Volterra integral equations of the second kind. SIAM J. Numer. Anal. 20, 569–579 (1983)

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