Download or read book The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 1976-06-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations written by A.A. Ivanov and published by Springer. This book was released on 2010-12-30 with total page 330 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Application and Numerical Solution of Integral Equations written by R.S. Anderssen and published by Springer. This book was released on 1980-03-31 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: This publication reports the proceedings of a one-day seminar on The Application and Numerical Solution of Integral Equations held at the Australian National University on Wednesday, November 29, 1978. It was organized by the Computing Research Group, Australian National University and the Division of Mathematics and Statistics, CSIRO. Due to unforeseen circumstances, Dr M.L. Dow was unable to participate. At short notice, Professor D. Elliott reviewed Cauchy singular integral equations, but a paper on same is not included in these proceedings. The interested reader is referred to the recent translation of V.V. Ivanov, The Theory of Approximate Methods and their Application to the Numerical Solution of Singular Integral Equations, Noordhoff International Publishers, Leyden, 1976. An attempt was made to structure the program to the extent that the emphasis was on the numerical solution of integral equations for which known applications exist along with explanations of how and why integral equation formalisms arise. In addition, the programme reflected the broad classification of most integral equations as either singular or non singular, as either Fredholm or Volterra and as either first or second kind.

Download or read book Solution Methods for Integral Equations written by M. A. Goldberg and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 351 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Computational Methods for Linear Integral Equations written by Prem Kythe and published by Springer Science & Business Media. This book was released on 2011-06-28 with total page 525 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical methods and computational aspects for linear integral equations. Such equations occur in various areas of applied mathematics, physics, and engineering. The material covered in this book, though not exhaustive, offers useful techniques for solving a variety of problems. Historical information cover ing the nineteenth and twentieth centuries is available in fragments in Kantorovich and Krylov (1958), Anselone (1964), Mikhlin (1967), Lonseth (1977), Atkinson (1976), Baker (1978), Kondo (1991), and Brunner (1997). Integral equations are encountered in a variety of applications in many fields including continuum mechanics, potential theory, geophysics, electricity and mag netism, kinetic theory of gases, hereditary phenomena in physics and biology, renewal theory, quantum mechanics, radiation, optimization, optimal control sys tems, communication theory, mathematical economics, population genetics, queue ing theory, and medicine. Most of the boundary value problems involving differ ential equations can be converted into problems in integral equations, but there are certain problems which can be formulated only in terms of integral equations. A computational approach to the solution of integral equations is, therefore, an essential branch of scientific inquiry.

Download or read book Singular Integral Equations written by E.G. Ladopoulos and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 569 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.

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 466 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.

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 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 Singular Integral Operators written by Solomon G. Mikhlin and published by Springer Science & Business Media. This book was released on 1987 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: The present edition differs from the original German one mainly in the following addi tional material: weighted norm inequalities for maximal functions and singular opera tors (§ 12, Chap. XI), polysingular integral operators and pseudo-differential operators (§§ 7, 8, Chap. XII), and spline approximation methods for solving singular integral equations (§ 4, Chap. XVII). Furthermore, we added two subsections on polynomial approximation methods for singular integral equations over an interval or with dis continuous coefficients (Nos. 3.6 and 3.7, Chap. XVII). In many places we incorporated new results which, in the vast majority, are from the last five years after publishing the German edition (note that the references are enlarged by about 150 new titles). S. G. Mikhlin wrote §§ 7, 8, Chap. XII, and the other additions were drawn up by S. Prossdorf. We wish to express our deepest gratitude to Dr. A. Bottcher and Dr. R. Lehmann who together translated the text into English carefully and with remarkable expertise.

Download or read book One Dimensional Linear Singular Integral Equations written by I. Gohberg and published by Birkhäuser. This book was released on 2012-12-06 with total page 263 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to the theory of linear one-dimensional singular integral equations. It is essentually a graduate textbook. Singular integral equations have attracted more and more attention, because, on one hand, this class of equations appears in many applications and, on the other, it is one of a few classes of equations which can be solved in explicit form. In this book material of the monograph [2] of the authors on one-dimensional singular integral operators is widely used. This monograph appeared in 1973 in Russian and later in German translation [3]. In the final text version the authors included many addenda and changes which have in essence changed character, structure and contents of the book and have, in our opinion, made it more suitable for a wider range of readers. Only the case of singular integral operators with continuous coefficients on a closed contour is considered herein. The case of discontinuous coefficients and more general contours will be considered in the second volume. We are grateful to the editor Professor G. Heinig of the volume and to the translators Dr. B. Luderer and Dr. S. Roch, and to G. Lillack, who did the typing of the manuscript, for the work they have done on this volume.

Download or read book The Birth of Numerical Analysis written by Adhemar Bultheel and published by World Scientific. This book was released on 2010 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: The 1947 paper by John von Neumann & Herman Goldstine, 'Numerical Inverting of Matrices of High Order', is considered as the birth certificate of numerical analysis. Since its publication, the evolution of this domain has been enormous. This book collects contributions by researchers who have lived through this evolution.

Download or read book Convolution Equations and Projection Methods for Their Solution written by Israel Gohberg and published by American Mathematical Soc.. This book was released on 2005-09-26 with total page 274 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.

Download or read book Finite Element Analysis of Composite Laminates written by O.O. Ochoa and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 222 pages. Available in PDF, EPUB and Kindle. Book excerpt: Composite materials are increasingly used in aerospace, underwater, and automotive structures. To take advantage of the full potential of composite materials, structural analysts and designers must have accurate mathematical models and design methods at their disposal. The objective of this monograph is to present the laminated plate theories and their finite element models to study the deformation, strength and failure of composite structures. Emphasis is placed on engineering aspects, such as the analytical descriptions, effective analysis tools, modeling of physical features, and evaluation of approaches used to formulate and predict the response of composite structures. The first chapter presents an overview of the text. Chapter 2 is devoted to the introduction of the definitions and terminology used in composite materials and structures. Anisotropic constitutive relations and Iaminate plate theories are also reviewed. Finite element models of laminated composite plates are presented in Chapter 3. Numerical evaluation of element coefficient matrices, post-computation of strains and stresses, and sample examples of laminated plates in bending and vibration are discussed. Chapter 4 introduces damage and failure criteria in composite laminates. Finally, Chapter 5 is dedicated to case studies involving various aspects and types of composite structures. Joints, cutouts, woven composites, environmental effects, postbuckling response and failure of composite laminates are discussed by considering specific examples.

Download or read book The Atmospheric Boundary Layer for Engineers written by R. S. Azad and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 589 pages. Available in PDF, EPUB and Kindle. Book excerpt: While I was participating in the IUTAM Symposium on Structure of Turbulence and Drag Reduction in Zurich, Switzerland, in 1989, I was approached by Prof. Dr. Themistocles Dracos to give a course oflectures on the Atmospheric Boundary Layer during my sabbatical leave at Eidgenossische Technische Hochschule (ETH) Zurich - Hoenggerberg in 1991. His reason for the suggestion was the growing interest in the environment and its dynamics created by flow in the Atmospheric Boundary Layer. I have been teaching boundary layer to undergraduate and graduate students for more than twenty five years, so I agreed to give a series of lectures on boundary layer of the atmosphere. From the start I thought very seriously about the problem and consulted all the published works in English on the Atmospheric Boundary Layer (ABL). First consider the topography of the Earth which has oceans calm and turbulent, mountain ranges of height up to 9 km, lands of variable height with forests, food growing vegetable and deserts. The shape of the Earth is nearly spherical except at the north and south poles. Sun supplies the energy to drive circulation of air around the Earth's atmosphere which for all practical purposes occupies the region up to about 10 to 11 km. This brief scenerio of Earth's topography reveals the complexity of flow very close to the Earth's surface that is hardly flat except at the oceans' surface which consists of about 70% of the total Earth's surface.

Download or read book Advances in Structural Optimization written by José Herskovits and published by Springer Science & Business Media. This book was released on 1995 with total page 530 pages. Available in PDF, EPUB and Kindle. Book excerpt: This text presents the techniques for a wide set of applications, ranging from the problems of size and shape optimization (historically the first to be studied) to topology and material optimization. Structural models are considered that use both discrete and finite elements. Structural materials can be classical or new. Emerging methods are also addressed, such as automatic differentiation, intelligent structures optimization, integration of structural optimization in concurrent engineering environments, and multidisciplinary optimization.