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Wavelet Based Numerical Methods For Some Boundary Value Problems
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Book Synopsis Wavelet Numerical Method and Its Applications in Nonlinear Problems by : You-He Zhou
Download or read book Wavelet Numerical Method and Its Applications in Nonlinear Problems written by You-He Zhou and published by Springer Nature. This book was released on 2021-03-09 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Wavelet Based Approximation Schemes for Singular Integral Equations by : Madan Mohan Panja
Download or read book Wavelet Based Approximation Schemes for Singular Integral Equations written by Madan Mohan Panja and published by CRC Press. This book was released on 2020-06-07 with total page 476 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
Book Synopsis Wavelet Methods for Elliptic Partial Differential Equations by : Karsten Urban
Download or read book Wavelet Methods for Elliptic Partial Differential Equations written by Karsten Urban and published by Numerical Mathematics and Scie. This book was released on 2009 with total page 509 pages. Available in PDF, EPUB and Kindle. Book excerpt: Wavelet methods are by now a well-known tool in image processing (jpeg2000). These functions have been used successfully in other areas, however. Elliptic Partial Differential Equations which model several processes in, for example, science and engineering, is one such field. This book, based on the author's course, gives an introduction to wavelet methods in general and then describes their application for the numerical solution of elliptic partial differential equations. Recently developed adaptive methods are also covered and each scheme is complemented with numerical results , exercises, and corresponding software.
Download or read book Haar Wavelets written by Ülo Lepik and published by Springer Science & Business Media. This book was released on 2014-01-09 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Harmonic Analysis by : María Cristina Pereyra
Download or read book Harmonic Analysis written by María Cristina Pereyra and published by American Mathematical Soc.. This book was released on 2012 with total page 437 pages. Available in PDF, EPUB and Kindle. Book excerpt: Conveys the remarkable beauty and applicability of the ideas that have grown from Fourier theory. It presents for an advanced undergraduate and beginning graduate student audience the basics of harmonic analysis, from Fourier's study of the heat equation, and the decomposition of functions into sums of cosines and sines (frequency analysis), to dyadic harmonic analysis, and the decomposition of functions into a Haar basis (time localization).
Download or read book Wavelets written by John J. Benedetto and published by CRC Press. This book was released on 2021-07-28 with total page 586 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Fractals and Fractional Calculus in Continuum Mechanics by : Alberto Carpinteri
Download or read book Fractals and Fractional Calculus in Continuum Mechanics written by Alberto Carpinteri and published by Springer. This book was released on 2014-05-04 with total page 352 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is characterized by the illustration of cases of fractal, self-similar and multi-scale structures taken from the mechanics of solid and porous materials, which have a technical interest. In addition, an accessible and self-consistent treatment of the mathematical technique of fractional calculus is provided, avoiding useless complications.
Book Synopsis Wavelet Methods for Dynamical Problems by : S. Gopalakrishnan
Download or read book Wavelet Methods for Dynamical Problems written by S. Gopalakrishnan and published by CRC Press. This book was released on 2010-03-17 with total page 299 pages. Available in PDF, EPUB and Kindle. Book excerpt: Employs a Step-by-Step Modular Approach to Structural ModelingConsidering that wavelet transforms have also proved useful in the solution and analysis of engineering mechanics problems, up to now there has been no sufficiently comprehensive text on this use. Wavelet Methods for Dynamical Problems: With Application to Metallic, Composite and Nano-co
Book Synopsis Numerical Methods in Scientific Computing by : Germund Dahlquist
Download or read book Numerical Methods in Scientific Computing written by Germund Dahlquist and published by SIAM. This book was released on 2008-01-01 with total page 742 pages. Available in PDF, EPUB and Kindle. Book excerpt: This new book from the authors of the classic book Numerical methods addresses the increasingly important role of numerical methods in science and engineering. More cohesive and comprehensive than any other modern textbook in the field, it combines traditional and well-developed topics with other material that is rarely found in numerical analysis texts, such as interval arithmetic, elementary functions, operator series, convergence acceleration, and continued fractions. Although this volume is self-contained, more comprehensive treatments of matrix computations will be given in a forthcoming volume. A supplementary Website contains three appendices: an introduction to matrix computations; a description of Mulprec, a MATLAB multiple precision package; and a guide to literature, algorithms, and software in numerical analysis. Review questions, problems, and computer exercises are also included. For use in an introductory graduate course in numerical analysis and for researchers who use numerical methods in science and engineering.
Book Synopsis Applied Functional Analysis by : Abul Hasan Siddiqi
Download or read book Applied Functional Analysis written by Abul Hasan Siddiqi and published by CRC Press. This book was released on 2003-09 with total page 536 pages. Available in PDF, EPUB and Kindle. Book excerpt: The methods of functional analysis have helped solve diverse real-world problems in optimization, modeling, analysis, numerical approximation, and computer simulation. Applied Functional Analysis presents functional analysis results surfacing repeatedly in scientific and technological applications and presides over the most current analytical and numerical methods in infinite-dimensional spaces. This reference highlights critical studies in projection theorem, Riesz representation theorem, and properties of operators in Hilbert space and covers special classes of optimization problems. Supported by 2200 display equations, this guide incorporates hundreds of up-to-date citations.
Book Synopsis Computational Methods in Engineering Boundary Value Problems by : T.Y. Na
Download or read book Computational Methods in Engineering Boundary Value Problems written by T.Y. Na and published by Academic Press. This book was released on 1980-01-18 with total page 321 pages. Available in PDF, EPUB and Kindle. Book excerpt: Computational Methods in Engineering Boundary Value Problems
Book Synopsis Numerical Solution of Boundary Value Problems for Ordinary Differential Equations by : Uri M. Ascher
Download or read book Numerical Solution of Boundary Value Problems for Ordinary Differential Equations written by Uri M. Ascher and published by SIAM. This book was released on 1994-12-01 with total page 620 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.
Book Synopsis Mathematical Theory of Subdivision by : Sandeep Kumar
Download or read book Mathematical Theory of Subdivision written by Sandeep Kumar and published by CRC Press. This book was released on 2019-07-09 with total page 247 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides good coverage of the powerful numerical techniques namely, finite element and wavelets, for the solution of partial differential equation to the scientists and engineers with a modest mathematical background. The objective of the book is to provide the necessary mathematical foundation for the advanced level applications of these numerical techniques. The book begins with the description of the steps involved in finite element and wavelets-Galerkin methods. The knowledge of Hilbert and Sobolev spaces is needed to understand the theory of finite element and wavelet-based methods. Therefore, an overview of essential content such as vector spaces, norm, inner product, linear operators, spectral theory, dual space, and distribution theory, etc. with relevant theorems are presented in a coherent and accessible manner. For the graduate students and researchers with diverse educational background, the authors have focused on the applications of numerical techniques which are developed in the last few decades. This includes the wavelet-Galerkin method, lifting scheme, and error estimation technique, etc. Features: • Computer programs in Mathematica/Matlab are incorporated for easy understanding of wavelets. • Presents a range of workout examples for better comprehension of spaces and operators. • Algorithms are presented to facilitate computer programming. • Contains the error estimation techniques necessary for adaptive finite element method. This book is structured to transform in step by step manner the students without any knowledge of finite element, wavelet and functional analysis to the students of strong theoretical understanding who will be ready to take many challenging research problems in this area.
Book Synopsis Scientific and Technical Aerospace Reports by :
Download or read book Scientific and Technical Aerospace Reports written by and published by . This book was released on 1994 with total page 568 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Advances in Mathematical Modelling, Applied Analysis and Computation by : Jagdev Singh
Download or read book Advances in Mathematical Modelling, Applied Analysis and Computation written by Jagdev Singh and published by Springer Nature. This book was released on 2022-10-13 with total page 632 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a valuable source for graduate students and researchers and provides a comprehensive introduction to recent theories and applications of mathematical modeling and numerical simulation. It includes selected peer-reviewed papers presented at the 4th International Conference on Mathematical Modelling, Applied Analysis and Computation (ICMMAAC 2021), held at JECRC University, Jaipur, India, during August 5–7, 2021. The book is focused on mathematical modeling of various problems arising in science and engineering and new efficient numerical approaches for solving linear nonlinear problems and rigorous mathematical theories, which can be used to analyze different kinds of mathematical models. Applications of mathematical methods in physics, chemistry, biology, mechanical engineering, civil engineering, computer science, social science, and finance are presented.
Book Synopsis Numerical Methods for Nonlinear Elliptic Differential Equations by : Klaus Böhmer
Download or read book Numerical Methods for Nonlinear Elliptic Differential Equations written by Klaus Böhmer and published by Oxford University Press. This book was released on 2010-10-07 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: Boehmer systmatically handles the different numerical methods for nonlinear elliptic problems.
Book Synopsis Wavelets Theory and Its Applications by : Mani Mehra
Download or read book Wavelets Theory and Its Applications written by Mani Mehra and published by Springer. This book was released on 2018-11-03 with total page 185 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
