Volume 6, Issue 4
Superconvergence of Galerkin Solutions for Hammerstein Equations
DOI:

Int. J. Numer. Anal. Mod., 6 (2009), pp. 696-710

Published online: 2009-06

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• 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.

• Keywords

Superconvergence interpolation post-processing iterated Galerkin method Hammerstein equations smooth and weakly singular kernels

• AMS Subject Headings

65B05 45L10

@Article{IJNAM-6-696, author = {Q. Huang and H. Xie}, title = {Superconvergence of Galerkin Solutions for Hammerstein Equations}, journal = {International Journal of Numerical Analysis and Modeling}, year = {2009}, volume = {6}, number = {4}, pages = {696--710}, 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. }, issn = {2617-8710}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/ijnam/792.html} }