Modelling, Analysis and Simulation Computing complex Airy functions by numerical quadrature
نویسندگان
چکیده
Integral representations are onsidered of solutions of the Airy di erential equation w z w = 0 for omputing Airy fun tions for omplex values of z. In a rst method ontour integral representations of the Airy fun tions are written as non-os illating integrals for obtaining stable representations, whi h are evaluated by the trapezoidal rule. In a se ond method an integral representation is evaluated by using generalized GaussLaguerre quadrature; this approa h provides a fast method for omputing Airy fun tions to a predetermined a ura y. Comparisons are made with well-known algorithms of Amos, designed for omputing Bessel fun tions of omplex argument. Several dis repan ies with Amos' ode are dete ted, and it is pointed out for whi h regions of the omplex plane Amos' ode is less a urate than the quadrature algorithms. Hints are given in order to build reliable software for omplex Airy fun tions. 2000 Mathemati s Subje t Classi ation: 33C10, 33F05, 41A60, 30E10, 65D20, 65D32.
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