An $hp$-spectral collocation method for nonlinear Volterra integral equations with vanishing variable delays
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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.References
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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
- 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).
- © Copyright 2015 American Mathematical Society
- Journal: Math. Comp. 85 (2016), 635-666
- MSC (2010): Primary 65L60, 45D05, 41A10, 65L70
- DOI: https://doi.org/10.1090/mcom/3023
- MathSciNet review: 3434874