High precision methods in eigenvalue problems and their applications
by Akulenko, L. D., (Leonid Denisovich)
This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems th…
Read More ↓Title Statements
- Full title :High precision methods in eigenvalue problems and their applications / Leonid D. Akulenko, Sergei V. Nesterov.
Summary
This book presents a survey of analytical, asymptotic, numerical, and combined methods of solving eigenvalue problems. It considers the new method of accelerated convergence for solving problems of the Sturm-Liouville type as well as boundary-value problems with boundary conditions of the first, second, and third kind. The authors also present high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and consider numerous eigenvalue problems that appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics,
Read More ↓Edition Statements
- Publication Date:2005.
Publication Statements
- Publisher(s):Chapman & Hall/CRC
- Place of Publication:Boca Raton
- Language:eng
- Publication Date:2005.
Notes
Description based upon print version of record.
The Physical Object
- Description:1 online resource (260 p.).
Edition Identifiers
- ISBN:0429220766, 9780429220760, 1280240415, 9781280240416, 9786610240418, 6610240418
- DOI:10.1201/9780203401286
- oclc:on1328354652
- LC Classification:QA379
- Dewey Decimal:512.9/436
Table of Contents
Front Cover; Contents; Preface; Authors; BASIC NOTATIONS; 1. Statement of Eigenvalue Problems. Basic Methods of Their Solution; 2. The Method of Accelerated Convergence for the Sturm-Liouville Problem; 3. Approximate Analytical Solution of Perturbed Eigenvalue Problems; 4. Generalized Sturm-Liouville Problem; 5. Asymptotics of Eigenvalues and Eigenfunctions of the Generalized Sturm-Liouville Problem for Higher Vibration Modes; 6. Solutions of Fourth-Order Self-Conjugate Problems. Oscillation Properties
7. The Method of Accelerated Convergence for Eigenvalue Problems for Fourth-Order Equations8. Perturbation Method in Eigenvalue Problems for Fourth-Order Equations; 9. Sturm-Liouville Problems for Vector-Valued Functions; 10. Vibrations and Stability of Elastic Systems; 11. Surface and Internal Waves in Heavy Ideal Fluid; 12. Parametric Vibrations of One-Dimensional Systems; 13. Vibrations of a Distributed Inhomogeneous System in a Rectangular Domain; 14. Free Vibrations of a Rectangular Membrane with Sharply Varying Surface Density
15. Free Vibrations of Elastic Systems in Elliptic DomainsReferences; Index
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Akulenko, L. D., (Leonid Denisovich)
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