Applied Singular Integral Equations

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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.

Multidimensional Singular Integrals And Integral Equations

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Author : S. G. Mikhlin
language : en
Publisher: Elsevier
Release Date : 2014-07-10

Multidimensional Singular Integrals And Integral Equations written by S. G. Mikhlin and has been published by Elsevier this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-07-10 with Mathematics categories.

Multidimensional Singular Integrals and Integral Equations presents the results of the theory of multidimensional singular integrals and of equations containing such integrals. Emphasis is on singular integrals taken over Euclidean space or in the closed manifold of Liapounov and equations containing such integrals. This volume is comprised of eight chapters and begins with an overview of some theorems on linear equations in Banach spaces, followed by a discussion on the simplest properties of multidimensional singular integrals. Subsequent chapters deal with compounding of singular integrals; properties of the symbol, with particular reference to Fourier transform of a kernel and the symbol of a singular operator; singular integrals in Lp spaces; and singular integral equations. The differentiation of integrals with a weak singularity is also considered, along with the rule for the multiplication of the symbols in the general case. The final chapter describes several applications of multidimensional singular integral equations to boundary problems in mathematical physics. This book will be of interest to mathematicians and students of mathematics.

Singular Integral Equations

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Author : E.G. Ladopoulos
language : en
Publisher: Springer Science & Business Media
Release Date : 2013-03-09

Singular Integral Equations written by E.G. Ladopoulos 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 2013-03-09 with Computers categories.

The present book deals with the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations, which are currently used in many fields of engineering mechanics with applied character, like elasticity, plasticity, thermoelastoplasticity, viscoelasticity, viscoplasticity, fracture mechanics, structural analysis, fluid mechanics, aerodynamics and elastodynamics. These types of singular integral equations form the latest high technology on the solution of very important problems of solid and fluid mechanics and therefore special attention should be given by the reader of the present book, who is interested for the new technology of the twentieth-one century. Chapter 1 is devoted with a historical report and an extended outline of References, for the finite-part singular integral equations, the multidimensional singular integral equations and the non-linear singular integral equations. Chapter 2 provides a finite-part singular integral representation analysis in Lp spaces and in general Hilbert spaces. In the same Chapter are investigated all possible approximation methods for the numerical evaluation of the finite-part singular integral equations, as closed form solutions for the above type of integral equations are available only in simple cases. Also, Chapter 2 provides further a generalization of the well known Sokhotski-Plemelj formulae and the Nother theorems, for the case of a finite-part singular integral equation.

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.

Singular Integrals In Boundary Element Methods

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Author : Vladimír Sládek
language : en
Publisher: Computational Mechanics
Release Date : 1998

Singular Integrals In Boundary Element Methods written by Vladimír Sládek and has been published by Computational Mechanics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1998 with Mathematics categories.

A text in singular integrals in boundary element methods. Topics covered include: treatment in crack problems; regularization of boundary integral equations by the derivative transfer method; regularization and evaluation of singular domain integrals in boundary element methods and others.

Solution Methods For Integral Equations

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Author : M. A. Goldberg
language : en
Publisher: Springer
Release Date : 1979-11

Solution Methods For Integral Equations written by M. A. Goldberg and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 1979-11 with Juvenile Nonfiction categories.

Singular Integral Equations And Discrete Vortices

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Author : Ivan K. Lifanov
language : en
Publisher: VSP
Release Date : 1996

Singular Integral Equations And Discrete Vortices written by Ivan K. Lifanov and has been published by VSP this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996 with Mathematics categories.

This monograph is divided into five parts and opens with elements of the theory of singular integral equation solutions in the class of absolutely integrable and non-integrable functions. The second part deals with elements of potential theory for the Helmholtz equation, especially with the reduction of Dirichlet and Neumann problems for Laplace and Helmholtz equations to singular integral equations. Part three contains methods of calculation for different one-dimensional and two-dimensional singular integrals. In this part, quadrature formulas of discrete vortex pair type in the plane case and closed vortex frame type in the spatial case for singular integrals are described for the first time. These quadrature formulas are applied to numerical solutions of singular integral equations of the 1st and 2nd kind with constant and variable coefficients, in part four of the book. Finally, discrete mathematical models of some problems in aerodynamics, electrodynamics and elasticity theory are given.

Integral Equations In Elasticity

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Author : Vladimir Zalmanovich Parton
language : en
Publisher:
Release Date : 1982

Integral Equations In Elasticity written by Vladimir Zalmanovich Parton and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1982 with Boundary value problems categories.

Proceedings Of 4th International Conference On Applied Numerical Modeling

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Author :
language : en
Publisher: Univelt
Release Date : 1985

Proceedings Of 4th International Conference On Applied Numerical Modeling written by and has been published by Univelt this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Technology & Engineering categories.

Applied Mathematics

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Author :
language : en
Publisher:
Release Date : 2008

Applied Mathematics written by and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008 with Mathematics categories.