Filon-Clenshaw-Curtis rules and their improvements for computing oscillatory integrals

A review of Filon-Clenshaw-Curtis (FCC) rules for oscillatory integrals and their improvements is given. These include FCC rules for linear oscillators, FCC rules for nonlinear oscillators and singular oscillatory integrals, modi ed FCC (MFCC) rules which do not deal with the inverse of the oscillator, and two versions of a scheme which combines MFCC rules with (double) exponential transformations in order to improve the stability of the rules

Keywords:

Oscillatory integral , Filon-Clenshaw-Curtis rules , Modi ed Filon-Clenshaw-Curtis rules , Exponential transformation