# American Institute of Mathematical Sciences

June  2006, 5(2): 395-413. doi: 10.3934/cpaa.2006.5.395

## Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations

 1 Institute of Applied Mathematics, University of Tartu, Liivi 2, 50409 Tartu, Estonia, Estonia

Received  March 2005 Revised  June 2005 Published  March 2006

We discuss a possibility to construct high order numerical algorithms on uniform or mildly graded grids for solving linear Fredholm integral equations of the second kind with weakly singular or other nonsmooth kernels. We first regularise the solution of the integral equation by introducing a suitable new independent variable and then solve the transformed equation by piecewise polynomial collocation and Galerkin methods on a mildly graded or uniform grid.
Citation: A. Pedas, G. Vainikko. Smoothing transformation and piecewise polynomial projection methods for weakly singular Fredholm integral equations. Communications on Pure & Applied Analysis, 2006, 5 (2) : 395-413. doi: 10.3934/cpaa.2006.5.395
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