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Algorithm 838: Airy functions. (English) Zbl 1070.65510
Summary: We present a Fortran 90 module, which computes the solutions and their derivatives of Airy’s differential equation, both on the real line and in the complex plane. The module also computes the zeros and associated values of the solutions and their derivatives, and the modulus and phase functions on the negative real axis. The computational methods are numerical integration of the differential equation and summation of asymptotic expansions for large argument. These methods were chosen because they are simple, adaptable to any precision, and amenable to rigorous error analysis. The module can be used to validate other codes or as a component in programs that require Airy functions.
MSC:
65D20Computation of special functions, construction of tables
33C10Bessel and Airy functions, cylinder functions, 0 F 1
33F05Numerical approximation and evaluation of special functions
33-04Machine computation, programs (special functions)
65Y15Packaged methods in numerical analysis
Software:
Algorithm 838