Hypersingular Integral Equations And Their Applications
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Hypersingular Integral Equations And Their Applications
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Author : I.K. Lifanov
language : en
Publisher: CRC Press
Release Date : 2003-12-29
Hypersingular Integral Equations And Their Applications written by I.K. Lifanov and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003-12-29 with Mathematics categories.
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
Hypersingular Integrals And Their Applications
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Author : Stefan Samko
language : en
Publisher: CRC Press
Release Date : 2001-10-25
Hypersingular Integrals And Their Applications written by Stefan Samko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2001-10-25 with Mathematics categories.
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.
The Numerical Solution Of Integral Equations Of The Second Kind
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Author : Kendall E. Atkinson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-28
The Numerical Solution Of Integral Equations Of The Second Kind written by Kendall E. Atkinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-28 with Mathematics categories.
This book provides an extensive introduction to the numerical solution of a large class of integral equations.
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.
Hypersingular Integral Equations In Fracture Analysis
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Author : Whye-Teong Ang
language : en
Publisher: Elsevier
Release Date : 2014-04-23
Hypersingular Integral Equations In Fracture Analysis written by Whye-Teong Ang and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-23 with Technology & Engineering categories.
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 problems - Gives hypersingular integral equations for selected crack problems in complete form - Lists computer codes in FORTRAN for the numerical solution of hypersingular integral equations
Topics In Integral And Integro Differential Equations
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Author : Harendra Singh
language : en
Publisher: Springer Nature
Release Date : 2021-03-15
Topics In Integral And Integro Differential Equations written by Harendra Singh and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-03-15 with Technology & Engineering categories.
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
14th Chaotic Modeling And Simulation International Conference
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Author : Christos H. Skiadas
language : en
Publisher: Springer Nature
Release Date : 2022-06-13
14th Chaotic Modeling And Simulation International Conference written by Christos H. Skiadas and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2022-06-13 with Science categories.
Gathering the proceedings of the 14th CHAOS2021 International Conference, this book highlights recent developments in nonlinear, dynamical and complex systems. The conference was intended to provide an essential forum for Scientists and Engineers to exchange ideas, methods, and techniques in the field of Nonlinear Dynamics, Chaos, Fractals and their applications in General Science and the Engineering Sciences. The respective chapters address key methods, empirical data and computer techniques, as well as major theoretical advances in the applied nonlinear field. Beyond showcasing the state of the art, the book will help academic and industrial researchers alike apply chaotic theory in their studies. Chapter "On the Origin of the Universe: Chaos or Cosmos" is available open access under a Creative Commons Attribution 4.0 International License via link.springer.com
Applied Singular Integral Equations
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Author : B. N. Mandal
language : en
Publisher: CRC Press
Release Date : 2016-04-19
Applied Singular Integral Equations written by B. N. Mandal and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-04-19 with Mathematics categories.
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.
Thirteen Papers In Analysis
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Author : American Mathem American Mathem
language : en
Publisher: American Mathematical Soc.
Release Date : 1987-12-30
Thirteen Papers In Analysis written by American Mathem American Mathem 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 1987-12-30 with Mathematics categories.
Differential And Integral Inequalities
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Author : Dorin Andrica
language : en
Publisher: Springer Nature
Release Date : 2019-11-14
Differential And Integral Inequalities written by Dorin Andrica and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-14 with Mathematics categories.
Theories, methods and problems in approximation theory and analytic inequalities with a focus on differential and integral inequalities are analyzed in this book. Fundamental and recent developments are presented on the inequalities of Abel, Agarwal, Beckenbach, Bessel, Cauchy–Hadamard, Chebychev, Markov, Euler’s constant, Grothendieck, Hilbert, Hardy, Carleman, Landau–Kolmogorov, Carlson, Bernstein–Mordell, Gronwall, Wirtinger, as well as inequalities of functions with their integrals and derivatives. Each inequality is discussed with proven results, examples and various applications. Graduate students and advanced research scientists in mathematical analysis will find this reference essential to their understanding of differential and integral inequalities. Engineers, economists, and physicists will find the highly applicable inequalities practical and useful to their research.