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Haar Wavelets: With Applications

Kataloginformation Katalogdatensatz500185558 .

Kataloginformation
Feldname	Details
Vorliegende Sprache	eng
ISBN	978-3-319-04294-7
Name	Lepik, Ülo
Name	Hein, Helle
Name ANZEIGE DER KETTE	Hein, Helle
T I T E L	Haar Wavelets
Zusatz zum Titel	With Applications
Verlagsort	Cham [u.a.]
Verlag	Springer
Erscheinungsjahr	2014
Erscheinungsjahr	2014
Umfang	Online-Ressource (X, 207 p. 50 illus, online resource)
Reihe	Mathematical Engineering
Notiz / Fußnoten	Description based upon print version of record
Weiterer Inhalt	Preface; Contents; 1 Preliminaries; 1.1 Why we Need the Wavelets?; 1.2 Wavelet Families; References; 2 Haar Wavelets; 2.1 Haar Wavelets and their Integrals; 2.2 Haar Matrices; 2.3 Expanding Functions into the Haar Wavelet Series; 2.4 Non-uniform Haar Wavelets; 2.5 Algorithms and Programs; 2.6 Related Papers; References; 3 Solution of Ordinary Differential Equations (ODEs); 3.1 Initial Value Problem for n-th Order ODE; 3.2 Treatment of Boundary Value Problems; 3.3 A Modified Solution; 3.4 Benefits of the Non-uniform Haar Wavelets; 3.5 Nonlinear Equations; 3.6 Method of Segmentation. 3.7 Related PapersReferences; 4 Stiff Equations; 4.1 Introduction; 4.2 Linear Problems; 4.3 Nonlinear Equations; 4.4 Robertson's Problem; 4.5 Singular Perturbation Problems; 4.6 Related Papers; References; 5 Integral Equations; 5.1 Introduction; 5.2 Fredholm Integral Equation; 5.3 Eigenvalues and Eigenfunctions; 5.4 Volterra Integral Equation; 5.5 Integro-Differential Equation; 5.6 Weakly Singular Integral Equations; 5.7 The Case of the Infinite Interval of Integration; 5.8 Nonlinear Integro-Differential Equation. 5.9 Application of the Integro-Differential Equations for Solving Boundary Value Problems of ODE5.10 Nonlinear Fredholm Integral Equation; 5.11 Related Papers; References; 6 Evolution Equations; 6.1 Problem Statement and Methods of Solution; 6.2 Diffusion Equation; 6.3 Burgers Equation; 6.4 Sine-Gordon Equation; 6.5 Related Papers; References; 7 Solving PDEs with the Aid of Two-Dimensional Haar Wavelets; 7.1 Problem Statement and Method of Solution; 7.2 Diffusion Equation; 7.3 Poisson Equation; 7.4 Related Papers; References; 8 Fractional Calculus; 8.1 Introduction. 8.2 About the Fractional Calculus8.3 Fractional Volterra Integral Equation; 8.4 Fractional Harmonic Vibrations; 8.5 Fractional Fredholm Integral Equation; 8.6 Haar Wavelet Operational Method for Solving Fractional ODEs; 8.7 Related Papers; References; 9 Applying Haar Wavelets in the Optimal Control Theory; 9.1 Basic Elements of Optimal Control; 9.2 Method of Solution; 9.3 Optimal Control with an Integral Constraint; 9.4 Optimal Control with a State Inequality Constraint; 9.5 Optimal Control with a Control Inequality Constraint; 9.6 Related Papers; References; 10 Buckling of Elastic Beams. 10.1 Problem Statement and Method of Solution10.2 Modelling Cracks; 10.3 Beam on Intermediate Supports; 10.4 Buckling of Cracked Beams; 10.5 Buckling of Beams of Variable Cross-Section; 10.6 Buckling of Beams on Elastic Foundation; 10.7 Related Papers; References; 11 Vibrations of Cracked Euler-Bernoulli Beams; 11.1 Governing Equations; 11.2 Bending of Multi-cracked Beams; 11.3 Free Vibrations of Beams with Singularities; 11.4 Forced Vibrations of the Beam; 11.5 Related Papers; References; 12 Free Vibrations on Non-uniform and Axially Functionally Graded Euler-Bernoulli Beams. 12.1 Governing Equations. PreliminariesHaar wavelets -- Solution of ordinary differential equations (ODEs) -- Stiff equations -- Integral equations -- Evolution equations -- Solving PDEs with the aid of two-dimensional Haar wavelets -- Fractional calculus -- Applying Haar wavelets in the optimal control theory -- Buckling of elastic beams -- Vibrations of cracked Euler-Bernoulli beams -- Free vibrations on non-uniform and axially functionally graded Euler-Bernoulli beams -- Vibrations of functionally graded Timoshenko beams -- Applying Haar wavelets in damage detection using machine learning methods.
Titelhinweis	Druckausg.ISBN: 978-331-90429-4-7
ISBN	ISBN 978-3-319-04295-4
Klassifikation	TGMD4
	TEC009070
	SCI018000
	*65T60
	65-01
	74S30
	00A06
	65L05
	65R20
	26A33
	65K10
	74K10
	74H45
	515.2433
	620
	TA355
	TA352-356
Kurzbeschreibung	This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions.
2. Kurzbeschreibung	This is the first book to present a systematic review of applications of the Haar wavelet method for solving Calculus and Structural Mechanics problems. Haar wavelet-based solutions for a wide range of problems, such as various differential and integral equations, fractional equations, optimal control theory, buckling, bending and vibrations of elastic beams are considered. Numerical examples demonstrating the efficiency and accuracy of the Haar method are provided for all solutions
SWB-Titel-Idn	400387360
Signatur	Springer E-Book
Bemerkungen	Elektronischer Volltext - Campuslizenz
Elektronische Adresse	$uhttp://dx.doi.org/10.1007/978-3-319-04295-4
Internetseite / Link	Volltext
Siehe auch	Volltext
Siehe auch	Cover
Siehe auch	Inhaltstext

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