Corrected finite difference eigenvalues of periodic Sturm–Liouville problems

✍ Scribed by D.J. Condon

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 78 KB
• Volume: 30
• Category: Article
• ISSN: 0168-9274
• DOI: 10.1016/s0168-9274(98)00093-2

✦ Synopsis

Computation of eigenvalues of regular Sturm-Liouville problems with periodic boundary conditions is considered. We show that a proof similar to that given by Andrew (1989) can be used to prove that a correction technique applied to a finite difference scheme given by Vanden Berghe et al. (1995) reduces the error in the kth eigenvalue estimate from O(k 4 h 2 ) to O(kh 2 ), where h is the uniform mesh length. We also provide a significantly shorter proof of a slightly weaker result.