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The Numerical Solution Of Linear First Kind Fredholm Integral Equations Using An Iterative Method
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Book Synopsis The Numerical Solution of Integral Equations of the Second Kind by : Kendall E. Atkinson
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.
Book Synopsis Linear Integral Equations by : Rainer Kress
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)
Book Synopsis Computational Methods for Integral Equations by : L. M. Delves
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.
Book Synopsis Linear and Nonlinear Integral Equations by : Abdul-Majid Wazwaz
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.
Book Synopsis Solution Methods for Integral Equations by : M. A. Goldberg
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:
Book Synopsis Computational Methods for Linear Integral Equations by : Prem Kythe
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.
Book Synopsis Numerical Methods for the Solution of Ill-Posed Problems by : A.N. Tikhonov
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.
Book Synopsis Numerical Solution of Integral Equations by : Michael A. Golberg
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.
Book Synopsis First Course In Integral Equations, A (Second Edition) by : Abdul-majid Wazwaz
Download or read book First Course In Integral Equations, A (Second Edition) written by Abdul-majid Wazwaz and published by World Scientific Publishing Company. This book was released on 2015-05-04 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition integrates the newly developed methods with classical techniques to give both modern and powerful approaches for solving integral equations. It provides a comprehensive treatment of linear and nonlinear Fredholm and Volterra integral equations of the first and second kinds. The materials are presented in an accessible and straightforward manner to readers, particularly those from non-mathematics backgrounds. Numerous well-explained applications and examples as well as practical exercises are presented to guide readers through the text. Selected applications from mathematics, science and engineering are investigated by using the newly developed methods.This volume consists of nine chapters, pedagogically organized, with six chapters devoted to linear integral equations, two chapters on nonlinear integral equations, and the last chapter on applications. It is intended for scholars and researchers, and can be used for advanced undergraduate and graduate students in applied mathematics, science and engineering.Click here for solutions manual.
Book Synopsis Fuzzy Mathematics: Approximation Theory by : George A. Anastassiou
Download or read book Fuzzy Mathematics: Approximation Theory written by George A. Anastassiou and published by Springer. This book was released on 2010-03-17 with total page 446 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph is the r st in Fuzzy Approximation Theory. It contains mostly the author s research work on fuzziness of the last ten years and relies a lot on [10]-[32] and it is a natural outgrowth of them. It belongs to the broader area of Fuzzy Mathematics. Chapters are self-contained and several advanced courses can be taught out of this book. We provide lots of applications but always within the framework of Fuzzy Mathematics. In each chapter is given background and motivations. A c- plete list of references is provided at the end. The topics covered are very diverse. In Chapter 1 we give an extensive basic background on Fuzziness and Fuzzy Real Analysis, as well a complete description of the book. In the following Chapters 2,3 we cover in deep Fuzzy Di?erentiation and Integ- tion Theory, e.g. we present Fuzzy Taylor Formulae. It follows Chapter 4 on Fuzzy Ostrowski Inequalities. Then in Chapters 5, 6 we present results on classical algebraic and trigonometric polynomial Fuzzy Approximation.
Book Synopsis Theoretical Numerical Analysis by : Kendall Atkinson
Download or read book Theoretical Numerical Analysis written by Kendall Atkinson and published by Springer Science & Business Media. This book was released on 2001-03-09 with total page 472 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives an introduction to functional analysis in a way that is tailored to fit the needs of the researcher or student. The book explains the basic results of functional analysis as well as relevant topics in numerical analysis. Applications of functional analysis are given by considering numerical methods for solving partial differential equations and integral equations. The material is especially useful for researchers and students who wish to work in theoretical numerical analysis and seek a background in the "tools of the trade" covered in this book.
Book Synopsis Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan by : Josef Dick
Download or read book Contemporary Computational Mathematics - A Celebration of the 80th Birthday of Ian Sloan written by Josef Dick and published by Springer. This book was released on 2018-05-23 with total page 1330 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is a tribute to Professor Ian Hugh Sloan on the occasion of his 80th birthday. It consists of nearly 60 articles written by international leaders in a diverse range of areas in contemporary computational mathematics. These papers highlight the impact and many achievements of Professor Sloan in his distinguished academic career. The book also presents state of the art knowledge in many computational fields such as quasi-Monte Carlo and Monte Carlo methods for multivariate integration, multi-level methods, finite element methods, uncertainty quantification, spherical designs and integration on the sphere, approximation and interpolation of multivariate functions, oscillatory integrals, and in general in information-based complexity and tractability, as well as in a range of other topics. The book also tells the life story of the renowned mathematician, family man, colleague and friend, who has been an inspiration to many of us. The reader may especially enjoy the story from the perspective of his family, his wife, his daughter and son, as well as grandchildren, who share their views of Ian. The clear message of the book is that Ian H. Sloan has been a role model in science and life.
Book Synopsis Proceedings of the 6th International Conference on Fundamental and Applied Sciences by : Samsul Ariffin Abdul Karim
Download or read book Proceedings of the 6th International Conference on Fundamental and Applied Sciences written by Samsul Ariffin Abdul Karim and published by Springer Nature. This book was released on 2022-01-05 with total page 775 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book highlights latest advancement in Mathematics, Physics and Chemistry. With the theme of “Innovative Science towards Sustainability and Industrial Revolution 4.0”, ICFAS 2020 brings together leading experts, scientific communities and industrialists working in the field of applied sciences and mathematics from all over the world to share the most recent developments and cutting-edge discoveries addressing sustainability and industrial revolution 4.0 in the field. The conference topics include green materials, molecular modelling, catalysis, nanodevices and nanosystems, smart materials applications, solar cells technology, computational mathematics, data analysis and visualization, and numerical analysis. The contents of this book are useful for researchers, students, and industrial practitioners in the areas of Mathematics, Physics and Chemistry as most of the topics are in line with IR 4.0.
Download or read book NBS Special Publication written by and published by . This book was released on 1968 with total page 398 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Energy Research Abstracts written by and published by . This book was released on 1993 with total page 490 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Regularization of Ill-Posed Problems by Iteration Methods by : S.F. Gilyazov
Download or read book Regularization of Ill-Posed Problems by Iteration Methods written by S.F. Gilyazov and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 348 pages. Available in PDF, EPUB and Kindle. Book excerpt: Iteration regularization, i.e., utilization of iteration methods of any form for the stable approximate solution of ill-posed problems, is one of the most important but still insufficiently developed topics of the new theory of ill-posed problems. In this monograph, a general approach to the justification of iteration regulari zation algorithms is developed, which allows us to consider linear and nonlinear methods from unified positions. Regularization algorithms are the 'classical' iterative methods (steepest descent methods, conjugate direction methods, gradient projection methods, etc.) complemented by the stopping rule depending on level of errors in input data. They are investigated for solving linear and nonlinear operator equations in Hilbert spaces. Great attention is given to the choice of iteration index as the regularization parameter and to estimates of errors of approximate solutions. Stabilizing properties such as smoothness and shape constraints imposed on the solution are used. On the basis of these investigations, we propose and establish efficient regularization algorithms for stable numerical solution of a wide class of ill-posed problems. In particular, descriptive regularization algorithms, utilizing a priori information about the qualitative behavior of the sought solution and ensuring a substantial saving in computational costs, are considered for model and applied problems in nonlinear thermophysics. The results of calculations for important applications in various technical fields (a continuous casting, the treatment of materials and perfection of heat-protective systems using laser and composite technologies) are given.
Book Synopsis Advances in Fuzzy Integral and Differential Equations by : Tofigh Allahviranloo
Download or read book Advances in Fuzzy Integral and Differential Equations written by Tofigh Allahviranloo and published by Springer Nature. This book was released on 2021-07-25 with total page 226 pages. Available in PDF, EPUB and Kindle. Book excerpt: As the title of the book suggests, the topics of this book are organized into two parts. The first part points out the fuzzy differential equations and the second one is related to the fuzzy integral equations. The book contains nine chapters that six chapters are about fuzzy differential equations and three of them are about fuzzy integral equations. In each part, the chapters’ authors are going to discuss the topics theoretically and numerically. All researchers and students in the field of mathematical, computer, and also engineering sciences can benefit from the subjects of the book.
