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We describe a method to evaluate integrals that arise in the asymptoticanalysis when two saddle points may be close together. These integrals, whichappear in problems from optics, acoustics or quantum mechanics as well as in awide class of special functions, can be transformed into Airy-type integralsand we use the trapezoidal rule to compute these integrals numerically. Thequadrature method, which remains valid when two saddle points coalesce, isillustrated with numerical examples.

Numerical evaluation of Airy-type integrals arising in uniform asymptotic analysis