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 - <p style="text-align: justify;">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.</p>