Abstract
In this paper a new iteration technique is proposed based on fast multiscale collocation methods of Chen et al. (SIAM J Numer Anal 40:344–375, 2002) for Fredholm integral equations of the second kind. It is shown that an additional order of convergence is obtained for each iteration even if the exact solution of the integral equation is non-smooth, the kernel of the integral operator is weakly singular and the matrix compression is implemented. When the solution is smooth, this leads to superconvergence. Numerical examples are presented to illustrate the theoretical results and the efficiency of the method.
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Acknowledgments
This work is partially supported by the Natural Science Foundation of China under grants 10771224 and 11071264, and the Guangdong Provincial Government of China through the “Computational Science Innovative Research Team” program to Zhongying Chen and Yongdong Zhang. This work is partially supported by the Natural Science Foundation of China under grant 11061008, the NSF of Guangxi Province under grant 2011GXNSFA018128, and Program for Excellent Talents in Guangxi Higher Education Institutions to Guangqing Long.
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Chen, Z., Long, G., Nelakanti, G. et al. Iterated Fast Collocation Methods for Integral Equations of the Second Kind. J Sci Comput 57, 502–517 (2013). https://doi.org/10.1007/s10915-013-9717-9
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DOI: https://doi.org/10.1007/s10915-013-9717-9