Wavelet Numerical Method and Its Applications in Nonlinear Problems (eBook)

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. 

Prof. You-He ZHOU received his bachelor's and master's degrees at Huazhong University of Science and Technology in 1982 and 1984, respectively, and Ph.D. degree at Lanzhou University in 1989. In 1999, he was appointed to a distinguished professor of the Cheung Kong Scholars Program by the Ministry of Education of China. He served as Founding Dean of the College of Civil Engineering and Mechanics of Lanzhou University during 2005-2017, a standing member of the Council of the Chinese Associate of Theoretical and Applied Mechanics, Associate Editor of Acta Mechanica Solida Sinica (Chinese Edition) and Founding Head of the Key Laboratory of Disaster and Environment in Western China of the Ministry of Education of China (Lanzhou University). Now, he serves as Dean of Superconducting Mechanics Research Institute of Lanzhou University, Head of Solid Mechanics Committee of the Council of the Chinese Associate of Theoretical and Applied Mechanics and Associate Editors of Chinese Journal of Theoretical and Applied Mechanics and Theoretical and Applied Mechanics Letters. His research interests are mainly concentrated in nonlinear mechanics. His research contributions were awarded two National Natural Science Prizes (second grade) and one National Scientific and Technology Development Prize (second grade) by the Chinese Central Government. His two serial academic papers published in IEEE Tran. Applied Superconductivity in 2007 received the Best Contribution Paper or the Von Duzer Prize awarded by the IEEE Superconducting Council. In 2019, his holding research project titled by 'Key methodologies of mechanics and applications for superconducting magnet design and fabrications' was awarded the first grade of Technical Invention Prize of the Ministry of Education of China. He holds the honors including the Well-Known Teacher of Higher-Education awarded by the Ministry of Education of China, the Outstanding Contributor for the Innovation of Western China awarded by the Chinese Association of Science and Technology, the Outstanding Young Scientist awarded by the Natural Science Foundation of China, etc. His teaching contributions were awarded one National Teaching Achievement Prize (second grade) by the Ministry of Education of China.

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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.