This article is cited in 7 papers

Calculation of solutions to the Mathieu equation and of related quantities

A. A. Abramov, S. V. Kurochkin

Dorodnicyn Computing Center, Russian Academy of Sciences, ul. Vavilova 40, Moscow, 119991, Russia

Abstract: 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.

Key words: Mathieu functions, oscillation theorems, recurrences, numerical stability.

UDC: 519.624.2+517.589

Received: 03.10.2006

 English version: Computational Mathematics and Mathematical Physics, 2007, 47:3, 397–406

Bibliographic databases:

• 
• 
•