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An $ hp$-spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays


Authors: Wang Zhong-qing and Sheng Chang-tao
Journal: Math. Comp. 85 (2016), 635-666
MSC (2010): Primary 65L60, 45D05, 41A10, 65L70
DOI: https://doi.org/10.1090/mcom/3023
Published electronically: September 2, 2015
MathSciNet review: 3434874
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Abstract: In this paper, we propose a multistep Legendre-Gauss spectral collocation method for nonlinear second-kind Volterra integral equations (VIEs) with vanishing variable delays. This method is easy to implement and possesses high-order accuracy. We also provide a rigorous convergence analysis of the $ hp$-version of the multistep spectral collocation method under $ L^2$-norm. Numerical results confirm the theoretical predictions.


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Additional Information

Wang Zhong-qing
Affiliation: School of Science, University of Shanghai for Science and Technology, Shanghai, 200093, People’s Republic of China — and — Division of Computational Science of E-institute of Shanghai Universities
Email: zqwang@usst.edu.cn

Sheng Chang-tao
Affiliation: School of Mathematical Sciences, Xiamen University, Xiamen, Fujian, 361005, People’s Republic of China

DOI: https://doi.org/10.1090/mcom/3023
Keywords: Multistep Legendre-Gauss spectral collocation method, nonlinear Volterra integral equations with vanishing variable delays, convergence analysis
Received by editor(s): October 6, 2013
Received by editor(s) in revised form: September 30, 2014
Published electronically: September 2, 2015
Additional Notes: This work was supported in part by NSF of China (grants 11571238 and 11171225), The Research Fund for Doctoral Program of Higher Education of China (grant 20133127110006), and The Fund for E-institute of Shanghai Universities (grant E03004).
Article copyright: © Copyright 2015 American Mathematical Society