Haar Wavelets: With Applications

ISBN-13: 9783319042947 / Angielski / Twarda / 2014 / 207 str.

Ulo Lepik; Helle Hein

Opis

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.

Recenzje

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)

Spis treści

Haar wavelets.- Application to ODE.- Stiff equations.- Integral equations.- Evolution equations.- Application to PDE.- Fractional differential and integral equations.- Application to optimal control theory.- Buckling of cracked Euler-Bernoulli elastic beams.- Bending and vibrations of elastic beams.- Buckling of functionally graded Euler-Bernoulli beams.- Vibrations of functionally graded Timoshenko beams.- Application to damage detection using machine learning.