On the double points of a Mathieu equation

✍ Scribed by P.N. Shivakumar; Jungong Xue

• Book ID: 104338951
• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 110 KB
• Volume: 107
• Category: Article
• ISSN: 0377-0427
• DOI: 10.1016/s0377-0427(99)00084-9

✦ Synopsis

For a Mathieu equation with parameter q, the eigenvalues can be regarded as functions of the variable q. Our aim is to ÿnd q when adjacent eigenvalues of the same type become equal yielding double points of the given Mathieu equation. The problem reduces to an equivalent eigenvalue problem of the form BX = X ; where B is an inÿnite tridiagonal matrix. A method is developed to locate the ÿrst double eigenvalue to any required degree of accuracy when q is an imaginary number. Computational results are given to illustrate the theory for the ÿrst double eigenvalue. Numerical results are given for some subsequent double points.