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Author : Yu Shi
Publisher :
ISBN 13 :
Total Pages : 160 pages
Book Rating : 4.:/5 (269 download)
Download or read book Numerical Methods for the Solution of Fredholm Integral Equations of the First Kind written by Yu Shi and published by . This book was released on 1992 with total page 160 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : Michael A. Golberg
Publisher : Springer Science & Business Media
ISBN 13 : 1489925937
Total Pages : 428 pages
Book Rating : 4.4/5 (899 download)
Download or read book Numerical Solution of Integral Equations written by Michael A. Golberg and published by Springer Science & Business Media. This book was released on 2013-11-11 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt: In 1979, I edited Volume 18 in this series: Solution Methods for Integral Equations: Theory and Applications. Since that time, there has been an explosive growth in all aspects of the numerical solution of integral equations. By my estimate over 2000 papers on this subject have been published in the last decade, and more than 60 books on theory and applications have appeared. In particular, as can be seen in many of the chapters in this book, integral equation techniques are playing an increas ingly important role in the solution of many scientific and engineering problems. For instance, the boundary element method discussed by Atkinson in Chapter 1 is becoming an equal partner with finite element and finite difference techniques for solving many types of partial differential equations. Obviously, in one volume it would be impossible to present a complete picture of what has taken place in this area during the past ten years. Consequently, we have chosen a number of subjects in which significant advances have been made that we feel have not been covered in depth in other books. For instance, ten years ago the theory of the numerical solution of Cauchy singular equations was in its infancy. Today, as shown by Golberg and Elliott in Chapters 5 and 6, the theory of polynomial approximations is essentially complete, although many details of practical implementation remain to be worked out.
Author : Kendall E. Atkinson
Publisher : Cambridge University Press
ISBN 13 : 0521583918
Total Pages : 572 pages
Book Rating : 4.5/5 (215 download)
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.
Author : John T. Jefferies
Publisher :
ISBN 13 :
Total Pages : 26 pages
Book Rating : 4.3/5 (91 download)
Download or read book The Numerical Solution of Fredholm Integral Equations of the First Kind written by John T. Jefferies and published by . This book was released on 1960 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Author : L. M. Delves
Publisher : CUP Archive
ISBN 13 : 9780521357968
Total Pages : 392 pages
Book Rating : 4.3/5 (579 download)
Download or read book Computational Methods for Integral Equations written by L. M. Delves and published by CUP Archive. This book was released on 1985 with total page 392 pages. Available in PDF, EPUB and Kindle. Book excerpt: This textbook provides a readable account of techniques for numerical solutions.
Author : G. Milton Wing
Publisher : SIAM
ISBN 13 : 0898712637
Total Pages : 141 pages
Book Rating : 4.8/5 (987 download)
Download or read book A Primer on Integral Equations of the First Kind written by G. Milton Wing and published by SIAM. This book was released on 1991-01-01 with total page 141 pages. Available in PDF, EPUB and Kindle. Book excerpt: Designed to offer applied mathematicians, physicists, chemists, engineers, geophysicists, an elementary level explanation of integral equations of the first kind.
Author : Grace Wahba
Publisher :
ISBN 13 :
Total Pages : 61 pages
Book Rating : 4.:/5 (227 download)
Download or read book On the Numerical Solution of Fredholm Integral Equations of the First Kind written by Grace Wahba and published by . This book was released on 1969 with total page 61 pages. Available in PDF, EPUB and Kindle. Book excerpt: The report is concerned with the numerical solution of a Fredholm integral equation of the first kind. Two methods in the literature seem to have resulted in satisfactory numerical examples. The first method is called the method of regularization of Tihonov and was studied experimentally by Tihonov and Glasko. The second method was discussed by Strand and Westwater and is called 'statistical estimation' of the solution. Both of these methods can be embedded in the general theory of the approximation of continuous linear functionals in a reproducing kernel Hilbert space. The overall purpose of this note is to demonstrate this statement in some considerable practical detail.
Author : M. A. Goldberg
Publisher : Springer Science & Business Media
ISBN 13 : 1475714661
Total Pages : 351 pages
Book Rating : 4.4/5 (757 download)
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:
Author : I. N. Dombrovskaja
Publisher :
ISBN 13 :
Total Pages : 11 pages
Book Rating : 4.:/5 (254 download)
Download or read book The Approximate Solution of Fredholm Integral Equations of the First Kind written by I. N. Dombrovskaja and published by . This book was released on 1966 with total page 11 pages. Available in PDF, EPUB and Kindle. Book excerpt: The instability of the solution of Fredholm integral equations of first kind leads to difficulties if one attempts to obtain approximate solutions by direct numerical procedures such as replacement by a finite algebraic system, or expansion in series. A stable problem is to obtain the best approximation to the solution of the integral equation by an element of some given compact set M. The element of M which satisfies this condition is called a "quasi-solution" of the integral equation. In this paper, a numerical method of approximating the quasi-solution is developed based on solving finite systems of equations in finite-dimensional subsets Mn of M. Convergence of the approximations obtained in this fashion to the quasi-solution is proved.
Author : Peter Linz
Publisher : SIAM
ISBN 13 : 9781611970852
Total Pages : 240 pages
Book Rating : 4.9/5 (78 download)
Download or read book Analytical and Numerical Methods for Volterra Equations written by Peter Linz and published by SIAM. This book was released on 1985-01-01 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents an aspect of activity in integral equations methods for the solution of Volterra equations for those who need to solve real-world problems. Since there are few known analytical methods leading to closed-form solutions, the emphasis is on numerical techniques. The major points of the analytical methods used to study the properties of the solution are presented in the first part of the book. These techniques are important for gaining insight into the qualitative behavior of the solutions and for designing effective numerical methods. The second part of the book is devoted entirely to numerical methods. The author has chosen the simplest possible setting for the discussion, the space of real functions of real variables. The text is supplemented by examples and exercises.
Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 3642214495
Total Pages : 639 pages
Book Rating : 4.6/5 (422 download)
Download or read book Linear and Nonlinear Integral Equations written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2011-11-24 with total page 639 pages. Available in PDF, EPUB and Kindle. Book excerpt: Linear and Nonlinear Integral Equations: Methods and Applications is a self-contained book divided into two parts. Part I offers a comprehensive and systematic treatment of linear integral equations of the first and second kinds. The text brings together newly developed methods to reinforce and complement the existing procedures for solving linear integral equations. The Volterra integral and integro-differential equations, the Fredholm integral and integro-differential equations, the Volterra-Fredholm integral equations, singular and weakly singular integral equations, and systems of these equations, are handled in this part by using many different computational schemes. Selected worked-through examples and exercises will guide readers through the text. Part II provides an extensive exposition on the nonlinear integral equations and their varied applications, presenting in an accessible manner a systematic treatment of ill-posed Fredholm problems, bifurcation points, and singular points. Selected applications are also investigated by using the powerful Padé approximants. This book is intended for scholars and researchers in the fields of physics, applied mathematics and engineering. It can also be used as a text for advanced undergraduate and graduate students in applied mathematics, science and engineering, and related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University in Chicago, Illinois, USA.
Author : Wolfgang Hackbusch
Publisher : Birkhäuser
ISBN 13 : 3034892152
Total Pages : 377 pages
Book Rating : 4.0/5 (348 download)
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.
Author : A.N. Tikhonov
Publisher : Springer Science & Business Media
ISBN 13 : 940158480X
Total Pages : 257 pages
Book Rating : 4.4/5 (15 download)
Download or read book Numerical Methods for the Solution of Ill-Posed Problems written by A.N. Tikhonov and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 257 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science, technology and engineering are posed in the form of operator equations of the first kind, with the operator and RHS approximately known. But such problems often turn out to be ill-posed, having no solution, or a non-unique solution, and/or an unstable solution. Non-existence and non-uniqueness can usually be overcome by settling for `generalised' solutions, leading to the need to develop regularising algorithms. The theory of ill-posed problems has advanced greatly since A. N. Tikhonov laid its foundations, the Russian original of this book (1990) rapidly becoming a classical monograph on the topic. The present edition has been completely updated to consider linear ill-posed problems with or without a priori constraints (non-negativity, monotonicity, convexity, etc.). Besides the theoretical material, the book also contains a FORTRAN program library. Audience: Postgraduate students of physics, mathematics, chemistry, economics, engineering. Engineers and scientists interested in data processing and the theory of ill-posed problems.
Author : R.S. Anderssen
Publisher : Springer
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)
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.
Author : Stephen M. Zemyan
Publisher : Springer Science & Business Media
ISBN 13 : 0817683496
Total Pages : 350 pages
Book Rating : 4.8/5 (176 download)
Download or read book The Classical Theory of Integral Equations written by Stephen M. Zemyan and published by Springer Science & Business Media. This book was released on 2012-07-10 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Classical Theory of Integral Equations is a thorough, concise, and rigorous treatment of the essential aspects of the theory of integral equations. The book provides the background and insight necessary to facilitate a complete understanding of the fundamental results in the field. With a firm foundation for the theory in their grasp, students will be well prepared and motivated for further study. Included in the presentation are: A section entitled Tools of the Trade at the beginning of each chapter, providing necessary background information for comprehension of the results presented in that chapter; Thorough discussions of the analytical methods used to solve many types of integral equations; An introduction to the numerical methods that are commonly used to produce approximate solutions to integral equations; Over 80 illustrative examples that are explained in meticulous detail; Nearly 300 exercises specifically constructed to enhance the understanding of both routine and challenging concepts; Guides to Computation to assist the student with particularly complicated algorithmic procedures. This unique textbook offers a comprehensive and balanced treatment of material needed for a general understanding of the theory of integral equations by using only the mathematical background that a typical undergraduate senior should have. The self-contained book will serve as a valuable resource for advanced undergraduate and beginning graduate-level students as well as for independent study. Scientists and engineers who are working in the field will also find this text to be user friendly and informative.
Author : Rainer Kress
Publisher : Springer Science & Business Media
ISBN 13 : 1461495938
Total Pages : 427 pages
Book Rating : 4.4/5 (614 download)
Download or read book Linear Integral Equations written by Rainer Kress and published by Springer Science & Business Media. This book was released on 2013-12-04 with total page 427 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book combines theory, applications, and numerical methods, and covers each of these fields with the same weight. In order to make the book accessible to mathematicians, physicists, and engineers alike, the author has made it as self-contained as possible, requiring only a solid foundation in differential and integral calculus. The functional analysis which is necessary for an adequate treatment of the theory and the numerical solution of integral equations is developed within the book itself. Problems are included at the end of each chapter. For this third edition in order to make the introduction to the basic functional analytic tools more complete the Hahn–Banach extension theorem and the Banach open mapping theorem are now included in the text. The treatment of boundary value problems in potential theory has been extended by a more complete discussion of integral equations of the first kind in the classical Holder space setting and of both integral equations of the first and second kind in the contemporary Sobolev space setting. In the numerical solution part of the book, the author included a new collocation method for two-dimensional hypersingular boundary integral equations and a collocation method for the three-dimensional Lippmann-Schwinger equation. The final chapter of the book on inverse boundary value problems for the Laplace equation has been largely rewritten with special attention to the trilogy of decomposition, iterative and sampling methods Reviews of earlier editions: "This book is an excellent introductory text for students, scientists, and engineers who want to learn the basic theory of linear integral equations and their numerical solution." (Math. Reviews, 2000) "This is a good introductory text book on linear integral equations. It contains almost all the topics necessary for a student. The presentation of the subject matter is lucid, clear and in the proper modern framework without being too abstract." (ZbMath, 1999)
Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 0203881052
Total Pages : 1143 pages
Book Rating : 4.2/5 (38 download)
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
