Wavelet Numerical Method And Its Applications In Nonlinear Problems PDF Download
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Author | : You-He Zhou |
Publisher | : |
Total Pages | : 0 |
Release | : 2021 |
Genre | : |
ISBN | : 9789813366442 |
Download Wavelet Numerical Method and Its Applications in Nonlinear Problems Book in PDF, ePub and Kindle
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author's own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering. .
Author | : A. Cohen |
Publisher | : Elsevier |
Total Pages | : 357 |
Release | : 2003-04-29 |
Genre | : Mathematics |
ISBN | : 0080537855 |
Download Numerical Analysis of Wavelet Methods Book in PDF, ePub and Kindle
Since their introduction in the 1980's, wavelets have become a powerful tool in mathematical analysis, with applications such as image compression, statistical estimation and numerical simulation of partial differential equations. One of their main attractive features is the ability to accurately represent fairly general functions with a small number of adaptively chosen wavelet coefficients, as well as to characterize the smoothness of such functions from the numerical behaviour of these coefficients. The theoretical pillar that underlies such properties involves approximation theory and function spaces, and plays a pivotal role in the analysis of wavelet-based numerical methods. This book offers a self-contained treatment of wavelets, which includes this theoretical pillar and it applications to the numerical treatment of partial differential equations. Its key features are: 1. Self-contained introduction to wavelet bases and related numerical algorithms, from the simplest examples to the most numerically useful general constructions. 2. Full treatment of the theoretical foundations that are crucial for the analysis of wavelets and other related multiscale methods : function spaces, linear and nonlinear approximation, interpolation theory. 3. Applications of these concepts to the numerical treatment of partial differential equations : multilevel preconditioning, sparse approximations of differential and integral operators, adaptive discretization strategies.
Author | : You-He Zhou |
Publisher | : Springer Nature |
Total Pages | : 478 |
Release | : 2021-03-09 |
Genre | : Technology & Engineering |
ISBN | : 9813366435 |
Download Wavelet Numerical Method and Its Applications in Nonlinear Problems Book in PDF, ePub and Kindle
This book summarizes the basic theory of wavelets and some related algorithms in an easy-to-understand language from the perspective of an engineer rather than a mathematician. In this book, the wavelet solution schemes are systematically established and introduced for solving general linear and nonlinear initial boundary value problems in engineering, including the technique of boundary extension in approximating interval-bounded functions, the calculation method for various connection coefficients, the single-point Gaussian integration method in calculating the coefficients of wavelet expansions and unique treatments on nonlinear terms in differential equations. At the same time, this book is supplemented by a large number of numerical examples to specifically explain procedures and characteristics of the method, as well as detailed treatments for specific problems. Different from most of the current monographs focusing on the basic theory of wavelets, it focuses on the use of wavelet-based numerical methods developed by the author over the years. Even for the necessary basic theory of wavelet in engineering applications, this book is based on the author’s own understanding in plain language, instead of a relatively difficult professional mathematical description. This book is very suitable for students, researchers and technical personnel who only want to need the minimal knowledge of wavelet method to solve specific problems in engineering.
Author | : Mani Mehra |
Publisher | : Springer |
Total Pages | : 182 |
Release | : 2018-11-03 |
Genre | : Mathematics |
ISBN | : 9811325952 |
Download Wavelets Theory and Its Applications Book in PDF, ePub and Kindle
This book provides comprehensive information on the conceptual basis of wavelet theory and it applications. Maintaining an essential balance between mathematical rigour and the practical applications of wavelet theory, the book is closely linked to the wavelet MATLAB toolbox, which is accompanied, wherever applicable, by relevant MATLAB codes. The book is divided into four parts, the first of which is devoted to the mathematical foundations. The second part offers a basic introduction to wavelets. The third part discusses wavelet-based numerical methods for differential equations, while the last part highlights applications of wavelets in other fields. The book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.
Author | : Santanu Saha Ray |
Publisher | : CRC Press |
Total Pages | : 273 |
Release | : 2018-01-12 |
Genre | : Mathematics |
ISBN | : 1351682229 |
Download Wavelet Methods for Solving Partial Differential Equations and Fractional Differential Equations Book in PDF, ePub and Kindle
The main focus of the book is to implement wavelet based transform methods for solving problems of fractional order partial differential equations arising in modelling real physical phenomena. It explores analytical and numerical approximate solution obtained by wavelet methods for both classical and fractional order partial differential equations.
Author | : John J. Benedetto |
Publisher | : CRC Press |
Total Pages | : 590 |
Release | : 2021-07-29 |
Genre | : Mathematics |
ISBN | : 1000446395 |
Download Wavelets Book in PDF, ePub and Kindle
Wavelets is a carefully organized and edited collection of extended survey papers addressing key topics in the mathematical foundations and applications of wavelet theory. The first part of the book is devoted to the fundamentals of wavelet analysis. The construction of wavelet bases and the fast computation of the wavelet transform in both continuous and discrete settings is covered. The theory of frames, dilation equations, and local Fourier bases are also presented. The second part of the book discusses applications in signal analysis, while the third part covers operator analysis and partial differential equations. Each chapter in these sections provides an up-to-date introduction to such topics as sampling theory, probability and statistics, compression, numerical analysis, turbulence, operator theory, and harmonic analysis. The book is ideal for a general scientific and engineering audience, yet it is mathematically precise. It will be an especially useful reference for harmonic analysts, partial differential equation researchers, signal processing engineers, numerical analysts, fluids researchers, and applied mathematicians.
Author | : Wolfgang Dahmen |
Publisher | : Elsevier |
Total Pages | : 587 |
Release | : 1997-08-13 |
Genre | : Mathematics |
ISBN | : 0080537146 |
Download Multiscale Wavelet Methods for Partial Differential Equations Book in PDF, ePub and Kindle
This latest volume in the Wavelets Analysis and Its Applications Series provides significant and up-to-date insights into recent developments in the field of wavelet constructions in connection with partial differential equations. Specialists in numerical applications and engineers in a variety of fields will find Multiscale Wavelet for Partial Differential Equations to be a valuable resource. Covers important areas of computational mechanics such as elasticity and computational fluid dynamics Includes a clear study of turbulence modeling Contains recent research on multiresolution analyses with operator-adapted wavelet discretizations Presents well-documented numerical experiments connected with the development of algorithms, useful in specific applications
Author | : Tao Qian |
Publisher | : Springer Science & Business Media |
Total Pages | : 567 |
Release | : 2007-02-24 |
Genre | : Mathematics |
ISBN | : 376437778X |
Download Wavelet Analysis and Applications Book in PDF, ePub and Kindle
This volume reflects the latest developments in the area of wavelet analysis and its applications. Since the cornerstone lecture of Yves Meyer presented at the ICM 1990 in Kyoto, to some extent, wavelet analysis has often been said to be mainly an applied area. However, a significant percentage of contributions now are connected to theoretical mathematical areas, and the concept of wavelets continuously stretches across various disciplines of mathematics. Key topics: Approximation and Fourier Analysis Construction of Wavelets and Frame Theory Fractal and Multifractal Theory Wavelets in Numerical Analysis Time-Frequency Analysis Adaptive Representation of Nonlinear and Non-stationary Signals Applications, particularly in image processing Through the broad spectrum, ranging from pure and applied mathematics to real applications, the book will be most useful for researchers, engineers and developers alike.
Author | : Ülo Lepik |
Publisher | : Springer Science & Business Media |
Total Pages | : 209 |
Release | : 2014-01-09 |
Genre | : Technology & Engineering |
ISBN | : 3319042955 |
Download Haar Wavelets Book in PDF, ePub and Kindle
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 | : G. Hariharan |
Publisher | : |
Total Pages | : 177 |
Release | : 2019 |
Genre | : Differential equations |
ISBN | : 9789813299610 |
Download Wavelet Solutions for Reaction-Diffusion Problems in Science and Engineering Book in PDF, ePub and Kindle
The book focuses on how to implement discrete wavelet transform methods in order to solve problems of reaction-diffusion equations and fractional-order differential equations that arise when modelling real physical phenomena. It explores the analytical and numerical approximate solutions obtained by wavelet methods for both classical and fractional-order differential equations; provides comprehensive information on the conceptual basis of wavelet theory and its applications; and strikes a sensible balance between mathematical rigour and the practical applications of wavelet theory. The book is divided into 11 chapters, the first three of which are devoted to the mathematical foundations and basics of wavelet theory. The remaining chapters provide wavelet-based numerical methods for linear, nonlinear, and fractional reaction-diffusion problems. Given its scope and format, the book is ideally suited as a text for undergraduate and graduate students of mathematics and engineering.