product quasi-interpolation method for weakly singular integral equation eigenvalue problem

adiscrete method of accuracyo(h^m) is constructed to solve the integral equation eigenvalue problem λφ(x) =ʃ¹ ₋₁ k(x, y)φ(y)dy, where k(x, y) = log|x−y| or k(x, y) = |x−y|^−α, 0<α<1, φ(x) being the eigenfunction associated with the eigenvalue λ. the method is based first on improving the boundary behavior of the exact solution φ(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 m.