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

Q. Huang & H. Xie

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

  • Copyright

COPYRIGHT: © Global Science Press

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@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} }
TY - JOUR T1 - Superconvergence of Galerkin Solutions for Hammerstein Equations AU - Q. Huang & H. Xie JO - International Journal of Numerical Analysis and Modeling VL - 4 SP - 696 EP - 710 PY - 2009 DA - 2009/06 SN - 6 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/ijnam/792.html KW - Superconvergence, interpolation post-processing, iterated Galerkin method, Hammerstein equations, smooth and weakly singular kernels. AB -

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.

Q. Huang and H. Xie. (2009). Superconvergence of Galerkin Solutions for Hammerstein Equations. International Journal of Numerical Analysis and Modeling. 6 (4). 696-710. doi:
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