Haar Wavelets With Applications /

• Main Authors: Lepik, Ülo (Author), Hein, Helle (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Cham : Springer International Publishing : Imprint: Springer, 2014.
• Series: Mathematical Engineering,
• Subjects: Engineering.; Integral equations.; System theory.; Computer mathematics.; Physics.; Vibration.; Dynamical systems.; Dynamics.; Vibration, Dynamical Systems, Control.; Systems Theory, Control.; Mathematical Methods in Physics.; Integral Equations.; Computational Science and 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 contr...

Table of Contents:

• 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.