Haar Wavelets: With Applications

by ïlo Lepik, Helle Hein

Overview

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.

Product Details

ISBN-13:	9783319344522
Publisher:	Springer International Publishing
Publication date:	02/14/2014
Series:	Mathematical Engineering
Edition description:	Softcover reprint of the original 1st ed. 2014
Pages:	207
Product dimensions:	6.10(w) x 9.25(h) x 0.02(d)

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.

Editorial Reviews

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)

From the Publisher