A Fast Wavelet Collocation Method for Integral Equations on Polygons
Yi Wang, Yuesheng Xu · Journal of Integral Equations and Applications · 2005
We develop a fast wavelet collocation method for solving Fredholm integral equations of the second kind with weakly singular kernels on polygons, following the general setting introduced in a recent paper [11].Specifically, we construct wavelet functions and multiscale collocation functionals having vanishing moments on polygons.Critical issues for numerical implementation of this method are considered, such as a practical matrix compression scheme, numerical integration of weakly singular integrals, error controls of numerical quadratures and numerical solutions of the resulting compressed linear systems.The estimate of the computational complexity ensures the proposed method is a fast algorithm.Numerical experiments are presented to demonstrate the proposed methods and confirm the theoretical estimates.2000