LAUSR

A class of Fredholm integral equations of the second kind, with respect to the exponential weight function $$w(x)=\exp (-(x^{-\alpha }+x^\beta ))$$w(x)=exp(-(x-α+xβ)), $$\alpha >0$$α>0, $$\beta >1$$β>1, on $$(0,+\infty )$$(0,+∞), is considered. The kernel k(x, y) and the function g(x) in such kind of equations, $$\begin{aligned} f(x)-\mu \int _0^{+\infty }k(x,y)f(y)w(y)\mathrm {d}y =g(x),\quad x\in (0,+\infty ), \end{aligned}$$f(x)-μ∫0+∞k(x,y)f(y)w(y)dy=g(x),x∈(0,+∞),can grow exponentially with respect to their arguments, when they approach to $$0^+$$0+ and/or $$+\infty $$+∞. We propose a simple and suitable Nyström-type method for solving these equations. The study of the stability and the convergence of this numerical method in based on our results on weighted polynomial approximation and “truncated” Gaussian rules, recently published in Mastroianni and Notarangelo (Acta Math Hung, 142:167–198, 2014), and Mastroianni, Milovanović and Notarangelo (IMA J Numer Anal 34:1654–1685, 2014) respectively. Moreover, we prove a priori error estimates and give some numerical examples. A comparison with other Nyström methods is also included.