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Int. J. Numer. Anal. Mod., 6 (2009), pp. 696-710. |
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Superconvergence of Galerkin solutions for Hammerstein equations Qiumei Huang 1, Hehu Xie 2 1 College of Applied Sciences, Beijing University of Technology, Beijing 100124, China.2 LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China. Received by the editors April 3, 2008 and, in revised form, July 10, 2009. Abstract
In the present paper, we discuss the superconvergence of the interpolated Galerkin solutions for Hammerstein equations. With the interpolation post-processing for the Galerkin approximation $x_h$, we get a higher order approximation $I_{2h}^{2r-1}x_h$, whose convergence order is the same as that of the iterated Galerkin solution. Such an interpolation post-processing method is much simpler than the iterated method especially for the weak singular kernel case. Some numerical experiments are carried out to demonstrate the effectiveness of the interpolation post-processing method. AMS subject classifications: 65B05, 45L10 Key words: Superconvergence, interpolation post-processing, iterated Galerkin method, Hammerstein equations, smooth and weakly singular kernels. Email: qmhuang@bjut.edu.cn, hhxie@lsec.cc.ac.cn |