Haar Wavelets

With Applications

Ülo Lepik, Helle Hein (Autoren)

Buch | Softcover

X, 207 Seiten

2016 | 1. Softcover reprint of the original 1st ed. 2014
Springer International Publishing (Verlag)
978-3-319-34452-2 (ISBN)

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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.

Preliminaries.- Haar 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.

From the reviews:

"This textbook presents a comprehensive overview of different applications of the Haar wavelet method. ... This useful book is mainly written for students and researchers in applied mathematics, physics and engineering. The authors demonstrate the efficiency and accuracy of the Haar wavelet method by numerous examples." (Manfred Tasche, zbMATH, Vol. 1287, 2014)

Erscheinungsdatum	01.09.2016
Reihe/Serie	Mathematical Engineering
Zusatzinfo	X, 207 p. 50 illus.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Themenwelt	Technik ► Maschinenbau
Schlagworte	computational science and engineering • Cybernetics and systems theory • damage detection • Engineering • Integral calculus and equations • Integral equations • Mathematical methods in physics • Mathematical Physics • Maths for scientists • mechanics of solids • Nonlinear Fredholm Integral Equation • Non-uniform Haar Wavelets • optimal control theory • Robertson's Problem • Robertson’s Problem • Systems Theory, Control • Vibration, Dynamical Systems, Control • Vibrations of Elastic Beams • Wavelet Families
ISBN-10	3-319-34452-8 / 3319344528
ISBN-13	978-3-319-34452-2 / 9783319344522
Zustand	Neuware