Evaluation of Cauchy principal value integrals of oscillatory kind

摘要

This paper studies the evaluation of Cauchy principal value (c.p.v.) integrals of oscillatory kind: ⨍⨍abf(x)x-τeiωxdx, where τ ∈ (a, b). The singularity of the c.p.v. integral is transferred to an individual oscillatory integral that can be analytically calculated. The remaining integral which is non-singular can be well calculated with a stable and fast quadrature method, namely the improved-Levin method. Numerical examples confirm the advantages of the proposed method.