A new version of the collocation method for a class of integral equations in the singular case (Q2434664)

The author studies a linear integral equation of the third kind with fixes singularities. The equation is of the form \[ Ax=x(t)\prod _{j=1}^l(t-t_j)^{m_j}+\int_{-1}^{+1} K(t,s).[(s+1)^{p_1}(1-s)^{p_2}]^{-1}x(s)ds=y(t). \] \(K\) and \(y\) are known continuous functions. The approximate solution is considered in the space of distributions, a new version of the collocation method based on use of special polynomials is suggested and justified.