Numerical solutions of integral equations on the half line. II: The Wiener-Hopf case
Numerical approximation schemes of quadrature type are investigated for integral equations of the form \[ x(s)-\int^{\infty}_{0}\kappa (s- t)x(t)dt=y(s),\quad 0\leq s<\infty. \] The principal hypotheses are that \(\kappa\) is integrable, bounded, and uniformly continuous on R, and that x and y are bounded and continuous or, alternatively, bounded and uniformly continuous, on \(R^+\). The convergence of numerical integration approximations is established, along with error bounds in some cases. The analysis involves the collectively compact operator approximation theory and a variant of that theory in which the role of compact sets is played by bounded uniformly equicontinuous sets of functions on \(R^+.\) [For part I see Numer. Math. 51, 599-614 (1987; Zbl 0613.65137).]
collectively compact operator approximation theory
scientific article; zbMATH DE number 4082927