A numerical evaluation of very oscillatory infinite integrals by asymptotics

摘要

Recently, Levin and Sidi have given some nonlinear methods for the accurate evaluation of slowly converging infinite integrals. But, one needs to solve some very instable linear systems, when, for example, the integrand have an increasingly rapid oscillatory behavior at infinity. In this work, we present a direct method, which avoids the instable linear systems.