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Ryabov, Yu. A.
Numeric-analytical construction of Mathieu functions. (English). Mathematica Bohemica, vol. 124 (1999), issue 1, pp. 15-28
MSC: 33E10, 34A25, 34A50, 65D15, 65D20 | MR 1687433 | Zbl 0936.65016 | DOI: 10.21136/MB.1999.125982
Keywords:
Mathieu functions; iterative algorithm; Quick-BASIC program; Fourier series
Summary:
In this paper we present an iterative algorithm for the construction of Mathieu functions of any order $N$ in the form of Fourier series (practically, polynomials), and also the corresponding Quick-BASIC program for realization of this algorithm with numerical values of the parameter.
References:
[1] Ch. Hayashi: Nonlinear Oscillations in Physical Systems. McGraw-Hill, New York, 1964. MR 0170071 | Zbl 0192.50605
[2] Yu. A. Ryabov: The estimations of convergence radius for series in power of parameter and algorithms for construction of Mathieu functions. Differencialnye uravnenija 15 (1979), no. 11, 1993-2003. (In Russian.) MR 0554259
[3] B. A. Grebenikov, Yu. A. Ryabov: Constructive methods in the analysis of nonlinear systems. Mir Publishers, Moscow, 1983, translated from Russian. MR 0733787 | Zbl 0536.65058
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