Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ODEs

• Published in: Нелінійні коливання
• Date: 2015
• Main Authors: Gavrilyuk, I.P., Makarov, V.L., Romanyuk, N.M.
• Format: Article
• Language: English
• Published: Інститут математики НАН України 2015
• Online Access: https://nasplib.isofts.kiev.ua/handle/123456789/177219
• Journal Title: Digital Library of Periodicals of National Academy of Sciences of Ukraine
• Cite this: Superexponentially convergent algorithm for an abstract eigenvalue problem with applications to ODEs / I.P. Gavrilyuk, V.L. Makarov, N.M. Romanyuk // Нелінійні коливання. — 2015. — Т. 18, № 3. — С. 332-356 — Бібліогр.: 23 назв. — англ.

A new algorithm for eigenvalue problems for the linear operators of the type A = A + B with a special application to high order ordinary differential equations is proposed and justified. The algorithm is based on the approximation of A by an operator A¯ = A + B¯ where the eigenvalue problem for A¯ i...