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High-Precision Methods in Eigenvalue Problems and Their Applications

Author: Leonid D. Akulenko

Publisher: CRC Press

Published: 2004-10-15

Total Pages: 260

ISBN-13: 113439022X

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

High Precision Methods in Eigenvalue Problems and Their Applications

Author: Leonid Denisovich Akulenko

Publisher: Taylor & Francis Group

Published: 2005

Total Pages: 239

ISBN-13: 9786610240418

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This book gives a survey of analytical, asymptotic, numerical and combined methods of solving eigenvalue problems. It considers a 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. This volume also presents high-precision asymptotic methods for determining eigenvalues and eigenfunctions of higher oscillation modes and considers numerous eigenvalue problems which appear in oscillation theory, acoustics, elasticity, hydrodynamics, geophysics, quantum mechanics, structural mechanics, electrodynamics and microelectronics.

High-Precision Methods in Eigenvalue Problems and Their Applications

Author: Leonid D. Akulenko

Publisher: CRC Press

Published: 2004-10-15

Total Pages: 261

ISBN-13: 020340128X

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Numerical Methods for Large Eigenvalue Problems

Author: Yousef Saad

Publisher: SIAM

Published: 2011-01-01

Total Pages: 292

ISBN-13: 9781611970739

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This revised edition discusses numerical methods for computing eigenvalues and eigenvectors of large sparse matrices. It provides an in-depth view of the numerical methods that are applicable for solving matrix eigenvalue problems that arise in various engineering and scientific applications. Each chapter was updated by shortening or deleting outdated topics, adding topics of more recent interest, and adapting the Notes and References section. Significant changes have been made to Chapters 6 through 8, which describe algorithms and their implementations and now include topics such as the implicit restart techniques, the Jacobi-Davidson method, and automatic multilevel substructuring.

Eigenvalue Problems: Algorithms, Software and Applications in Petascale Computing

Author: Tetsuya Sakurai

Publisher: Springer

Published: 2018-01-03

Total Pages: 312

ISBN-13: 3319624261

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This book provides state-of-the-art and interdisciplinary topics on solving matrix eigenvalue problems, particularly by using recent petascale and upcoming post-petascale supercomputers. It gathers selected topics presented at the International Workshops on Eigenvalue Problems: Algorithms; Software and Applications, in Petascale Computing (EPASA2014 and EPASA2015), which brought together leading researchers working on the numerical solution of matrix eigenvalue problems to discuss and exchange ideas – and in so doing helped to create a community for researchers in eigenvalue problems. The topics presented in the book, including novel numerical algorithms, high-performance implementation techniques, software developments and sample applications, will contribute to various fields that involve solving large-scale eigenvalue problems.

Symplectic Difference Systems: Oscillation and Spectral Theory

Author: Ondřej Došlý

Publisher: Springer Nature

Published: 2019-09-06

Total Pages: 593

ISBN-13: 303019373X

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This monograph is devoted to covering the main results in the qualitative theory of symplectic difference systems, including linear Hamiltonian difference systems and Sturm-Liouville difference equations, with the emphasis on the oscillation and spectral theory. As a pioneer monograph in this field it contains nowadays standard theory of symplectic systems, as well as the most current results in this field, which are based on the recently developed central object - the comparative index. The book contains numerous results and citations, which were till now scattered only in journal papers. The book also provides new applications of the theory of matrices in this field, in particular of the Moore-Penrose pseudoinverse matrices, orthogonal projectors, and symplectic matrix factorizations. Thus it brings this topic to the attention of researchers and students in pure as well as applied mathematics.

Aeroelastic Vibrations and Stability of Plates and Shells

Author: Sergey D. Algazin

Publisher: Walter de Gruyter GmbH & Co KG

Published: 2014-12-11

Total Pages: 234

ISBN-13: 3110338378

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Back-action of aerodynamics onto structures such as wings cause vibrations and may resonantly couple to them, thus causing instabilities (flutter) and endangering the whole structure. By careful choices of geometry, materials and damping mechanisms, hazardous effects on wind engines, planes, turbines and cars can be avoided. Besides an introduction into the problem of flutter, new formulations of flutter problems are given as well as a treatise of supersonic flutter and of a whole range of mechanical effects. Numerical and analytical methods to study them are developed and applied to the analysis of new classes of flutter problems for plates and shallow shells of arbitrary plane form. Specific problems discussed in the book in the context of numerical simulations are supplemented by Fortran code examples (available on the website).

Applications of Lie Groups to Difference Equations

Author: Vladimir Dorodnitsyn

Publisher: CRC Press

Published: 2010-12-01

Total Pages: 344

ISBN-13: 9781420083101

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Intended for researchers, numerical analysts, and graduate students in various fields of applied mathematics, physics, mechanics, and engineering sciences, Applications of Lie Groups to Difference Equations is the first book to provide a systematic construction of invariant difference schemes for nonlinear differential equations. A guide to methods

Recent Advances in Mechanics

Author: E.E. Gdoutos

Publisher: Springer Science & Business Media

Published: 2011-01-19

Total Pages: 459

ISBN-13: 9400705573

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This book contains 24 papers presented at the symposium on “Recent Advances in Mechanics” dedicated to the late Professor – Academician Pericles S. Theocaris in commemoration of the tenth anniversary of his death. The papers are written by world renowned and recognized experts in their fields and serve as a reference and guide for future research. The topics covered in the book can be divided into three major themes: Mathematical methods in applied mechanics (nine papers), experimental mechanics (nine papers) and fracture mechanics (six papers). Topics covered include: Application of reciprocity relations to laser-based ultrasonics, boundary value problems of the theory of elasticity, optimal design in contact mechanics, scaling of strength and lifetime distributions of quasibrittle structures, directional distortional hardening in plasticity, vibration of systems, instability phenomena in damped systems, variational methods for static and dynamic elasticity problems, an accelerated Newmark scheme for solving the equations of motion in the time domain, photoelastic tomography, electronic speckle pattern interferometry, composites exposed to fire, sampling moiré, microelecromechanical systems, experimental mechanics in nano-scale, advanced cement based nanocomposites, piezonuclear transmutations in brittle rocks under mechanical loading, stress triaxiality at crack tips studied by caustics, reinforcement of a cracked elastic plate with defects, some actual problems of fracture mechanics, cyclic plasticity with applications to extremely low cycle fatigue of structural steel, and fracture of a highly filled polymer composite.

Handbook of Ordinary Differential Equations

Author: Andrei D. Polyanin

Publisher: CRC Press

Published: 2017-11-15

Total Pages: 1496

ISBN-13: 1466569409

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The Handbook of Ordinary Differential Equations: Exact Solutions, Methods, and Problems, is an exceptional and complete reference for scientists and engineers as it contains over 7,000 ordinary differential equations with solutions. This book contains more equations and methods used in the field than any other book currently available. Included in the handbook are exact, asymptotic, approximate analytical, numerical symbolic and qualitative methods that are used for solving and analyzing linear and nonlinear equations. The authors also present formulas for effective construction of solutions and many different equations arising in various applications like heat transfer, elasticity, hydrodynamics and more. This extensive handbook is the perfect resource for engineers and scientists searching for an exhaustive reservoir of information on ordinary differential equations.