Quadrature methods for integral equations of the second kind over infinite intervals

Abstract

Convergence results are proved for a class of quadrature methods for integral equations of the form y ( t ) = f ( t ) + ∫ 0 ∞ k ( t , s ) y ( s ) d s y(t) = f(t) + \smallint _0^\infty \;k(t,s)y(s)\,ds . An important special case is the Nyström method, in which the integral term is approximated by an ordinary quadrature rule. For all of the methods considered here, the rate of convergence is the same, apart from a constant factor, as that of the quadrature approximation to the integral term.