Geodesic
Calculation of solutions to the Mathieu equation and of related quantities
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 414-423

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For the Mathieu equation, we consider finding eigenvalues with a given index (on the basis of oscillation theorems for the relevant difference equations), the stability of solutions to the difference equations, correct definition and calculation of eigenvalues and Mathieu functions with noninteger numbers, correct definition and calculation of the Mathieu characteristic exponent, and the calculation of values of solutions to the Mathieu equation for large arguments. Numerical algorithms are proposed for the problems listed above. 
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     title = {Calculation of solutions to the {Mathieu} equation and of related quantities},
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A. A. Abramov; S. V. Kurochkin. Calculation of solutions to the Mathieu equation and of related quantities. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 3, pp. 414-423. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_3_a4/