Numerical treatment of a class of systems of Fredholm integral equations on the real line (Q2871183)

The system of Fredholm integral equations, where the kernel consists of a product of a function \( h(x,y)\) with weight functions of the form NEWLINE\[NEWLINE w^{\alpha,\beta}(y)= | y|^{\alpha}e^{-| y|^{\beta}},\qquad \alpha >-1,\;\beta >1,NEWLINE\]NEWLINE can be rewritten as follows \( (I-K)f=g \).NEWLINENEWLINERegarding this equation in the Sobolev space of functions, the approximate solution is obtained using the Gaussian quadrature rule by the sequence of orthogonal polynomials \( P^{\alpha,\beta}_{m}(y)\) with the weights \(w^{\alpha,\beta}(y)\). The numerical method is applied to some systems of two and three integral equations.