Download or read book Hypersingular Integral Equations and Their Applications written by I.K. Lifanov and published by CRC Press. This book was released on 2003-12-29 with total page 416 pages. Available in PDF, EPUB and Kindle. Book excerpt: A number of new methods for solving singular and hypersingular integral equations have emerged in recent years. This volume presents some of these new methods along with classical exact, approximate, and numerical methods. The authors explore the analysis of hypersingular integral equations based on the theory of pseudodifferential operators and co
Download or read book Hypersingular Integrals and Their Applications written by Stefan Samko and published by CRC Press. This book was released on 2001-10-25 with total page 382 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before building more sophisticated ideas, and his discussions include a description of hypersingular integrals as they relate to functional spaces. Hypersingular Integrals and Their Applications also presents recent results and applications that will prove valuable to graduate students and researchers working in mathematical analysis.
Download or read book Hypersingular Integrals and Their Applications written by Stefan Samko and published by CRC Press. This book was released on 2001-10-25 with total page 378 pages. Available in PDF, EPUB and Kindle. Book excerpt: Hypersingular integrals arise as constructions inverse to potential-type operators and are realized by the methods of regularization and finite differences. This volume develops these approaches in a comprehensive treatment of hypersingular integrals and their applications. The author is a renowned expert on the topic. He explains the basics before
Download or read book Applied Singular Integral Equations written by B. N. Mandal and published by CRC Press. This book was released on 2016-04-19 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book is devoted to varieties of linear singular integral equations, with special emphasis on their methods of solution. It introduces the singular integral equations and their applications to researchers as well as graduate students of this fascinating and growing branch of applied mathematics.
Download or read book Handbook of Integral Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 2008-02-12 with total page 1143 pages. Available in PDF, EPUB and Kindle. Book excerpt: Unparalleled in scope compared to the literature currently available, the Handbook of Integral Equations, Second Edition contains over 2,500 integral equations with solutions as well as analytical and numerical methods for solving linear and nonlinear equations. It explores Volterra, Fredholm, WienerHopf, Hammerstein, Uryson, and other equa
Download or read book Integral Equations written by Wolfgang Hackbusch and published by Birkhäuser. This book was released on 2012-12-06 with total page 377 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of integral equations has been an active research field for many years and is based on analysis, function theory, and functional analysis. On the other hand, integral equations are of practical interest because of the «boundary integral equation method», which transforms partial differential equations on a domain into integral equations over its boundary. This book grew out of a series of lectures given by the author at the Ruhr-Universitat Bochum and the Christian-Albrecht-Universitat zu Kiel to students of mathematics. The contents of the first six chapters correspond to an intensive lecture course of four hours per week for a semester. Readers of the book require background from analysis and the foundations of numeri cal mathematics. Knowledge of functional analysis is helpful, but to begin with some basic facts about Banach and Hilbert spaces are sufficient. The theoretical part of this book is reduced to a minimum; in Chapters 2, 4, and 5 more importance is attached to the numerical treatment of the integral equations than to their theory. Important parts of functional analysis (e. g. , the Riesz-Schauder theory) are presented without proof. We expect the reader either to be already familiar with functional analysis or to become motivated by the practical examples given here to read a book about this topic. We recall that also from a historical point of view, functional analysis was initially stimulated by the investigation of integral equations.
Download or read book Topics in Integral and Integro Differential Equations written by Harendra Singh and published by Springer Nature. This book was released on 2021-04-16 with total page 255 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book includes different topics associated with integral and integro-differential equations and their relevance and significance in various scientific areas of study and research. Integral and integro-differential equations are capable of modelling many situations from science and engineering. Readers should find several useful and advanced methods for solving various types of integral and integro-differential equations in this book. The book is useful for graduate students, Ph.D. students, researchers and educators interested in mathematical modelling, applied mathematics, applied sciences, engineering, etc. Key Features • New and advanced methods for solving integral and integro-differential equations • Contains comparison of various methods for accuracy • Demonstrates the applicability of integral and integro-differential equations in other scientific areas • Examines qualitative as well as quantitative properties of solutions of various types of integral and integro-differential equations
Download or read book Boundary Integral Equations in Elasticity Theory written by A.M. Linkov and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 286 pages. Available in PDF, EPUB and Kindle. Book excerpt: by the author to the English edition The book aims to present a powerful new tool of computational mechanics, complex variable boundary integral equations (CV-BIE). The book is conceived as a continuation of the classical monograph by N. I. Muskhelishvili into the computer era. Two years have passed since the Russian edition of the present book. We have seen growing interest in numerical simulation of media with internal structure, and have evidence of the potential of the new methods. The evidence was especially clear in problems relating to multiple grains, blocks, cracks, inclusions and voids. This prompted me, when preparing the English edition, to place more emphasis on such topics. The other change was inspired by Professor Graham Gladwell. It was he who urged me to abridge the chain of formulae and to increase the number of examples. Now the reader will find more examples showing the potential and advantages of the analysis. The first chapter of the book contains a simple exposition of the theory of real variable potentials, including the hypersingular potential and the hypersingular equations. This makes up for the absence of such exposition in current textbooks, and reveals important links between the real variable BIE and the complex variable counterparts. The chapter may also help readers who are learning or lecturing on the boundary element method.
Download or read book Water Wave Scattering written by Birendra Nath Mandal and published by CRC Press. This book was released on 2015-05-21 with total page 375 pages. Available in PDF, EPUB and Kindle. Book excerpt: The theory of water waves is most varied and is a fascinating topic. It includes a wide range of natural phenomena in oceans, rivers, and lakes. It is mostly concerned with elucidation of some general aspects of wave motion including the prediction of behaviour of waves in the presence of obstacles of some special configurations that are of interes
Download or read book The Numerical Solution of Integral Equations of the Second Kind written by Kendall E. Atkinson and published by Cambridge University Press. This book was released on 1997-06-28 with total page 572 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides an extensive introduction to the numerical solution of a large class of integral equations.
Download or read book Hypersingular Integral Equations in Fracture Analysis written by Whye-Teong Ang and published by Woodhead Publishing. This book was released on 2017-11-13 with total page 212 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Hypersingular Integral Equations in Fracture Analysis" explains how plane elastostatic crack problems may be formulated and solved in terms of hypersingular integral equations. The unknown functions in the hypersingular integral equations are the crack opening displacements. Once the hypersingular integral equations are solved, the crack tip stress intensity factors, which play an important role in fracture analysis, may be easily computed. This title consists of six chapters: Elastic crack problems, fracture mechanics, equations of elasticity and finite-part integrals; Hypersingular integral equations for coplanar cracks in anisotropic elastic media; Numerical methods for solving hypersingular integral equations; Hypersingular boundary integral equation method for planar cracks in an anisotropic elastic body; A numerical Green's function boundary integral approach for crack problems; and Edge and curved cracks and piezoelectric cracks. This book provides a clear account of the hypersingular integral approach for fracture analysis, gives in complete form the hypersingular integral equations for selected crack problems, and lists FORTRAN programs of numerical methods for solving hypersingular integral equations. Explains the hypersingular integral approach using specific and progressively more complex crack problemsGives hypersingular integral equations for selected crack problems in complete formLists computer codes in FORTRAN for the numerical solution of hypersingular integral equations
Download or read book Integral Equations and Their Applications written by Matiur Rahman and published by WIT Press. This book was released on 2007 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.
Download or read book Large Truncated Toeplitz Matrices Toeplitz Operators and Related Topics written by Dario A. Bini and published by Birkhäuser. This book was released on 2017-03-21 with total page 740 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents a collection of expository and research papers on various topics in matrix and operator theory, contributed by several experts on the occasion of Albrecht Böttcher’s 60th birthday. Albrecht Böttcher himself has made substantial contributions to the subject in the past. The book also includes a biographical essay, a complete bibliography of Albrecht Böttcher’s work and brief informal notes on personal encounters with him. The book is of interest to graduate and advanced undergraduate students majoring in mathematics, researchers in matrix and operator theory as well as engineers and applied mathematicians.
Download or read book The Boundary Element Method Volume 1 written by L. C. Wrobel and published by John Wiley & Sons. This book was released on 2002-04-22 with total page 480 pages. Available in PDF, EPUB and Kindle. Book excerpt: The boundary element method (BEM) is a modern numerical techniquewhich has enjoyed increasing popularity over the last two decades,and is now an established alternative to traditional computationalmethods of engineering analysis. The main advantage of the BEM isits unique ability to provide a complete solution in terms ofboundary values only, with substantial savings in modelling effort. This two-volume book set is designed to provide the readers with acomprehensive and up-to-date account of the boundary element methodand its application to solving engineering problems. Each volume isa self-contained book including a substantial amount of materialnot previously covered by other text books on the subject. Volume 1covers applications to heat transfer, acoustics, electrochemistryand fluid mechanics problems, while volume 2 concentrates on solidsand structures, describing applications to elasticity, plasticity,elastodynamics, fracture mechanics and contact analysis. The earlychapters are designed as a teaching text for final yearundergraduate courses. Both volumes reflect the experience of theauthors over a period of more than twenty years of boundary element research. This volume, Applications in Thermo-Fluids and Acoustics, provides acomprehensive presentation of the BEM from fundamentals to advancedengineering applications and encompasses: Steady and transient heat transfer Potential and viscous fluid flows Frequency and time-domain acoustics Corrosion and other electrochemical problems. A unique feature of this book is an in-depth presentation of BEMformulations in all the above fields, including detaileddiscussions of the basic theory, numerical algorithms and practicalengineering applications of the method. Written by an internationally recognised authority in the field,this is essential reading for postgraduates, researchers andpractitioners in civil, mechanical and chemical engineering andapplied mathematics.
Download or read book Bessel Functions and Their Applications written by B G Korenev and published by CRC Press. This book was released on 2002-07-25 with total page 290 pages. Available in PDF, EPUB and Kindle. Book excerpt: Bessel functions are associated with a wide range of problems in important areas of mathematical physics. Bessel function theory is applied to problems of acoustics, radio physics, hydrodynamics, and atomic and nuclear physics. Bessel Functions and Their Applications consists of two parts. In Part One, the author presents a clear and rigorous intro
Download or read book Integral Operators in Non Standard Function Spaces written by Vakhtang Kokilashvili and published by Birkhäuser. This book was released on 2016-05-11 with total page 585 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book, the result of the authors' long and fruitful collaboration, focuses on integral operators in new, non-standard function spaces and presents a systematic study of the boundedness and compactness properties of basic, harmonic analysis integral operators in the following function spaces, among others: variable exponent Lebesgue and amalgam spaces, variable Hölder spaces, variable exponent Campanato, Morrey and Herz spaces, Iwaniec-Sbordone (grand Lebesgue) spaces, grand variable exponent Lebesgue spaces unifying the two spaces mentioned above, grand Morrey spaces, generalized grand Morrey spaces, and weighted analogues of some of them. The results obtained are widely applied to non-linear PDEs, singular integrals and PDO theory. One of the book's most distinctive features is that the majority of the statements proved here are in the form of criteria. The book is intended for a broad audience, ranging from researchers in the area to experts in applied mathematics and prospective students.
Download or read book The Navier Stokes Problem written by Alexander G. Ramm and published by Springer Nature. This book was released on 2022-06-01 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The main result of this book is a proof of the contradictory nature of the Navier‒Stokes problem (NSP). It is proved that the NSP is physically wrong, and the solution to the NSP does not exist on R+ (except for the case when the initial velocity and the exterior force are both equal to zero; in this case, the solution (, ) to the NSP exists for all ≥ 0 and (, ) = 0). It is shown that if the initial data 0() ≢ 0, (,) = 0 and the solution to the NSP exists for all ε R+, then 0() := (, 0) = 0. This Paradox proves that the NSP is physically incorrect and mathematically unsolvable, in general. Uniqueness of the solution to the NSP in the space 21(R3) × C(R+) is proved, 21(R3) is the Sobolev space, R+ = [0, ∞). Theory of integral equations and inequalities with hyper-singular kernels is developed. The NSP is reduced to an integral inequality with a hyper-singular kernel.
