A Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels

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• 作者：Guo He^a ; ^{heguo261@126.com" class="auth_mail" title="E-mail the corresponding author} ; Shuhuang Xiang^b ; ^{xiangsh@mail.csu.edu.cn" class="auth_mail" title="E-mail the corresponding author} ; Zhenhua Xu^c ; ^{xuzhenhua19860536@163.com" class="auth_mail" title="E-mail the corresponding author}
• 关键词：65D32 ; 65D99
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2016
• 出版时间：July 2016
• 年：2016
• 卷：300
• 期：Complete
• 页码：354-368
• 全文大小：589 K

文摘

Based on the Filon–Clenshaw–Curtis method for highly oscillatory integrals, and together with the Sommariva’s result (Sommariva, 2013) for Clenshaw–Curtis quadrature rule, we present a Chebyshev collocation method for a class of Fredholm integral equations with highly oscillatory kernels, whose unknown function is assumed to be less oscillatory than the kernel. In the proposed method, the Filon–Clenshaw–Curtis method is used to compute the involved oscillatory integrals, which makes the proposed method very precise. By solving only a small system of linear equations, we can obtain a very satisfactory numerical solution. The performance of the presented method is illustrated by several numerical examples. Compared with the method proposed by Li et al. (2012), this method enjoys a lower computational complexity. Furthermore, numerical examples show that the presented method has a competitive advantage on the accuracy compared with the method in Li et al. (2012).