Product quasi-interpolation method for weakly singular integral equation eigenvalue problem
A discrete method of accuracy O(h(m)) is constructed to solve the integral equation eigenvalue problem lambda phi(x) = integral(1)(-1) K(x, y)phi(y)dy, where K(x,y)= log vertical bar x - y vertical bar or K(x, y)=vertical bar x - y vertical bar(-alpha), 0 < alpha < 1, phi(x) being the eigenfunction associated with the eigenvalue lambda. The method is based first on improving the boundary behavior of the exact solution phi(x) with the help of a change of variables, and second on the product integration method based on a discrete spline quasi-interpolant (abbr. dQI) of order to. (C) 2010 IMACS. Published by Elsevier B.V. All rights reserved.
eigenvalue problem product integration methods spline quasi-interpolation