Wavelet Based Approximation Schemes For Singular Integral Equations
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Wavelet Based Approximation Schemes For Singular Integral Equations
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Author : Madan Mohan Panja
language : en
Publisher: CRC Press
Release Date : 2020-06-07
Wavelet Based Approximation Schemes For Singular Integral Equations written by Madan Mohan Panja and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-06-07 with Mathematics categories.
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.
Multiscale Wavelet Methods For Partial Differential Equations
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Author : Wolfgang Dahmen
language : en
Publisher: Elsevier
Release Date : 1997-08-13
Multiscale Wavelet Methods For Partial Differential Equations written by Wolfgang Dahmen and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-08-13 with Mathematics categories.
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
Integral Methods In Science And Engineering
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Author : Barbara S Bertram
language : en
Publisher: CRC Press
Release Date : 2019-05-20
Integral Methods In Science And Engineering written by Barbara S Bertram and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-05-20 with Mathematics categories.
Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells.
Integral Methods In Science And Engineering
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Author : Christian Constanda
language : en
Publisher: CRC Press
Release Date : 2020-01-16
Integral Methods In Science And Engineering written by Christian Constanda and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2020-01-16 with Mathematics categories.
Based on proceedings of the International Conference on Integral Methods in Science and Engineering, this collection of papers addresses the solution of mathematical problems by integral methods in conjunction with approximation schemes from various physical domains. Topics and applications include: wavelet expansions, reaction-diffusion systems, variational methods , fracture theory, boundary value problems at resonance, micromechanics, fluid mechanics, combustion problems, nonlinear problems, elasticity theory, and plates and shells. Volume 1 covers Analytic Methods.
Spline Functions And The Theory Of Wavelets
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Author : Serge Dubuc
language : en
Publisher: American Mathematical Soc.
Release Date : 1999-01-01
Spline Functions And The Theory Of Wavelets written by Serge Dubuc and has been published by American Mathematical Soc. this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-01-01 with Mathematics categories.
This work is based on a series of thematic workshops on the theory of wavelets and the theory of splines. Important applications are included. The volume is divided into four parts: Spline Functions, Theory of Wavelets, Wavelets in Physics, and Splines and Wavelets in Statistics. Part one presents the broad spectrum of current research in the theory and applications of spline functions. Theory ranges from classical univariate spline approximation to an abstract framework for multivariate spline interpolation. Applications include scattered-data interpolation, differential equations and various techniques in CAGD. Part two considers two developments in subdivision schemes; one for uniform regularity and the other for irregular situations. The latter includes construction of multidimensional wavelet bases and determination of bases with a given time frequency localization. In part three, the multifractal formalism is extended to fractal functions involving oscillating singularites. There is a review of a method of quantization of classical systems based on the theory of coherent states. Wavelets are applied in the domains of atomic, molecular and condensed-matter physics. In part four, ways in which wavelets can be used to solve important function estimation problems in statistics are shown. Different wavelet estimators are proposed in the following distinct cases: functions with discontinuities, errors that are no longer Gaussian, wavelet estimation with robustness, and error distribution that is no longer stationary. Some of the contributions in this volume are current research results not previously available in monograph form. The volume features many applications and interesting new theoretical developments. Readers will find powerful methods for studying irregularities in mathematics, physics, and statistics.
Numerical Analysis Of Wavelet Methods
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Author : Albert Cohen
language : en
Publisher: JAI Press
Release Date : 2003-06-26
Numerical Analysis Of Wavelet Methods written by Albert Cohen and has been published by JAI Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-06-26 with Mathematics categories.
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.
Wavelets Theory And Its Applications
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Author : Mani Mehra
language : en
Publisher: Springer
Release Date : 2018-11-03
Wavelets Theory And Its Applications written by Mani Mehra and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2018-11-03 with Mathematics categories.
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.
Singular Integral Equations
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Author : Ricardo Estrada
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Singular Integral Equations written by Ricardo Estrada and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-12-06 with Mathematics categories.
Many physical problems that are usually solved by differential equation techniques can be solved more effectively by integral equation methods. This work focuses exclusively on singular integral equations and on the distributional solutions of these equations. A large number of beautiful mathematical concepts are required to find such solutions, which in tum, can be applied to a wide variety of scientific fields - potential theory, me chanics, fluid dynamics, scattering of acoustic, electromagnetic and earth quake waves, statistics, and population dynamics, to cite just several. An integral equation is said to be singular if the kernel is singular within the range of integration, or if one or both limits of integration are infinite. The singular integral equations that we have studied extensively in this book are of the following type. In these equations f (x) is a given function and g(y) is the unknown function. 1. The Abel equation x x) = l g (y) d 0
Wavelet Analysis And Applications
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Author : Peter Roberts
language : en
Publisher: New Age International
Release Date : 2007
Wavelet Analysis And Applications written by Peter Roberts and has been published by New Age International this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007 with Wavelets (Mathematics) categories.
Wavelets And Related Functions Constitute A Most Recent Set Of Mathematical Tools, Impacting Many Branches Of Mathematical And Applied Sciences, Ranging From Approximation Theory And Harmonic Analysis To Signal Analysis And Image Compression.This Volume Includes Lectures Delivered At The Platinum Jubilee Workshop And Tenth Ramanujan Symposium, Pjwtrs-2003, On Wavelet Analysis, Conducted In March 2003. The Contents Cover A Variety Of Interesting Topics Like Wavelets As Approximation Tools, Connections With Filter Banks, The Bessel-Wavelet Transform, Relations With Partial Differential Equations Of Fluid Flow, Weyl Heisenberg Frames, Reconstruction Of Functions From Irregular Sampling And Various Applications, Particularly In Electrical Engineering. This Book Will Be Useful To Mathematicians, Computer And Electrical Engineers, Systems Analysts And Applied Scientists. The Level Can Be Graduate Engineer Or Post Graduate Student Of Mathematics.
The Theory Of Approximate Methods And Their Application To The Numerical Solution Of Singular Integral Equations
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Author : Viktor Viktorovich Ivanov
language : en
Publisher:
Release Date : 1976
The Theory Of Approximate Methods And Their Application To The Numerical Solution Of Singular Integral Equations written by Viktor Viktorovich Ivanov and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Approximation theory categories.