Haar Wavelets

With Applications
2014
ISBN: 978-3-319-04294-7
Verlag: Springer International Publishing

Buch, Englisch, 207 Seiten, HC runder Rücken kaschiert, Format (B × H): 160 mm x 241 mm, Gewicht: 4557 g

Reihe: Mathematical Engineering

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.

Zielgruppe

Research

Autoren/Hrsg.

Hein, Helle

Lepik, Ülo

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Signalverarbeitung
• Mathematik | Informatik Mathematik Mathematische Analysis Harmonische Analysis, Fourier-Mathematik
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Zerstörungsfreie Werkstoffprüfung
• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

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.