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Haar Wavelets: With Applications

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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.

Author(s): Ülo Lepik, Helle Hein (auth.)
Series: Mathematical Engineering
Edition: 1
Publisher: Springer International Publishing
Year: 2014

Language: English
Pages: 207
Tags: Vibration, Dynamical Systems, Control; Systems Theory, Control; Mathematical Methods in Physics; Integral Equations; Computational Science and Engineering

Front Matter....Pages i-x
Preliminaries....Pages 1-6
Haar Wavelets....Pages 7-20
Solution of Ordinary Differential Equations (ODEs)....Pages 21-43
Stiff Equations....Pages 45-57
Integral Equations....Pages 59-82
Evolution Equations....Pages 83-95
Solving PDEs with the Aid of Two-Dimensional Haar Wavelets....Pages 97-105
Fractional Calculus....Pages 107-122
Applying Haar Wavelets in the Optimal Control Theory....Pages 123-135
Buckling of Elastic Beams....Pages 137-149
Vibrations of Cracked Euler-Bernoulli Beams....Pages 151-165
Free Vibrations on Non-uniform and Axially Functionally Graded Euler-Bernoulli Beams....Pages 167-176
Vibrations of Functionally Graded Timoshenko Beams....Pages 177-187
Applying Haar Wavelets in Damage Detection Using Machine Learning Methods....Pages 189-202
Back Matter....Pages 203-207