The Approximate Solution Of Fredholm Integral Equations Of The First Kind

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First Course In Integral Equations, A (Second Edition)

Author : Abdul-majid Wazwaz
Publisher : World Scientific Publishing Company
ISBN 13 : 9814675148
Total Pages : 327 pages
Book Rating : 4.8/5 (146 download)

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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.

Partial Differential Equations and Solitary Waves Theory

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 364200251X
Total Pages : 700 pages
Book Rating : 4.6/5 (42 download)

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Book Synopsis Partial Differential Equations and Solitary Waves Theory by : Abdul-Majid Wazwaz

Download or read book Partial Differential Equations and Solitary Waves Theory written by Abdul-Majid Wazwaz and published by Springer Science & Business Media. This book was released on 2010-05-28 with total page 700 pages. Available in PDF, EPUB and Kindle. Book excerpt: "Partial Differential Equations and Solitary Waves Theory" is a self-contained book divided into two parts: Part I is a coherent survey bringing together newly developed methods for solving PDEs. While some traditional techniques are presented, this part does not require thorough understanding of abstract theories or compact concepts. Well-selected worked examples and exercises shall guide the reader through the text. Part II provides an extensive exposition of the solitary waves theory. This part handles nonlinear evolution equations by methods such as Hirota’s bilinear method or the tanh-coth method. A self-contained treatment is presented to discuss complete integrability of a wide class of nonlinear equations. This part presents in an accessible manner a systematic presentation of solitons, multi-soliton solutions, kinks, peakons, cuspons, and compactons. While the whole book can be used as a text for advanced undergraduate and graduate students in applied mathematics, physics and engineering, Part II will be most useful for graduate students and researchers in mathematics, engineering, and other related fields. Dr. Abdul-Majid Wazwaz is a Professor of Mathematics at Saint Xavier University, Chicago, Illinois, USA.

The Numerical Solution of Integral Equations of the Second Kind

Author : Kendall E. Atkinson
Publisher : Cambridge University Press
ISBN 13 : 0521583918
Total Pages : 572 pages
Book Rating : 4.5/5 (215 download)

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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.

Solving Frontier Problems of Physics: The Decomposition Method

Author : G. Adomian
Publisher : Springer Science & Business Media
ISBN 13 : 9401582890
Total Pages : 367 pages
Book Rating : 4.4/5 (15 download)

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Book Synopsis Solving Frontier Problems of Physics: The Decomposition Method by : G. Adomian

Download or read book Solving Frontier Problems of Physics: The Decomposition Method written by G. Adomian and published by Springer Science & Business Media. This book was released on 2013-06-29 with total page 367 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Adomian decomposition method enables the accurate and efficient analytic solution of nonlinear ordinary or partial differential equations without the need to resort to linearization or perturbation approaches. It unifies the treatment of linear and nonlinear, ordinary or partial differential equations, or systems of such equations, into a single basic method, which is applicable to both initial and boundary-value problems. This volume deals with the application of this method to many problems of physics, including some frontier problems which have previously required much more computationally-intensive approaches. The opening chapters deal with various fundamental aspects of the decomposition method. Subsequent chapters deal with the application of the method to nonlinear oscillatory systems in physics, the Duffing equation, boundary-value problems with closed irregular contours or surfaces, and other frontier areas. The potential application of this method to a wide range of problems in diverse disciplines such as biology, hydrology, semiconductor physics, wave propagation, etc., is highlighted. For researchers and graduate students of physics, applied mathematics and engineering, whose work involves mathematical modelling and the quantitative solution of systems of equations.

Linear Integral Equations

Author : Rainer Kress
Publisher : Springer Science & Business Media
ISBN 13 : 1461495938
Total Pages : 427 pages
Book Rating : 4.4/5 (614 download)

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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)

Introduction to Integral Equations with Applications

Author : Abdul J. Jerri
Publisher : John Wiley & Sons
ISBN 13 : 9780471317340
Total Pages : 458 pages
Book Rating : 4.3/5 (173 download)

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Book Synopsis Introduction to Integral Equations with Applications by : Abdul J. Jerri

Download or read book Introduction to Integral Equations with Applications written by Abdul J. Jerri and published by John Wiley & Sons. This book was released on 1999-09-03 with total page 458 pages. Available in PDF, EPUB and Kindle. Book excerpt: From the reviews of the First Edition: "Extremely clear, self-contained text . . . offers to a wide class of readers the theoretical foundations and the modern numerical methods of the theory of linear integral equations."-Revue Roumaine de Mathematiques Pures et Appliquées. Abdul Jerri has revised his highly applied book to make it even more useful for scientists and engineers, as well as mathematicians. Covering the fundamental ideas and techniques at a level accessible to anyone with a solid undergraduate background in calculus and differential equations, Dr. Jerri clearly demonstrates how to use integral equations to solve real-world engineering and physics problems. This edition provides precise guidelines to the basic methods of solutions, details more varied numerical methods, and substantially boosts the total of practical examples and exercises. Plus, it features added emphasis on the basic theorems for the existence and uniqueness of solutions of integral equations and points out the interrelation between differentiation and integration. Other features include: * A new section on integral equations in higher dimensions. * An improved presentation of the Laplace and Fourier transforms. * A new detailed section for Fredholm integral equations of the first kind. * A new chapter covering the basic higher quadrature numerical integration rules. * A concise introduction to linear and nonlinear integral equations. * Clear examples of singular integral equations and their solutions. * A student's solutions manual available directly from the author.

Linear and Nonlinear Integral Equations

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 3642214495
Total Pages : 639 pages
Book Rating : 4.6/5 (422 download)

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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.

Handbook of Integral Equations

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 0203881052
Total Pages : 1143 pages
Book Rating : 4.2/5 (38 download)

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Book Synopsis Handbook of Integral Equations by : Andrei D. Polyanin

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

Computational Methods for Integral Equations

Author : L. M. Delves
Publisher : CUP Archive
ISBN 13 : 9780521357968
Total Pages : 392 pages
Book Rating : 4.3/5 (579 download)

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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.

Numerical Solution of Integral Equations

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
ISBN 13 : 1489925937
Total Pages : 428 pages
Book Rating : 4.4/5 (899 download)

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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.

Linear Integral Equations

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 1461207657
Total Pages : 327 pages
Book Rating : 4.4/5 (612 download)

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Book Synopsis Linear Integral Equations by : Ram P. Kanwal

Download or read book Linear Integral Equations written by Ram P. Kanwal and published by Springer Science & Business Media. This book was released on 2013-11-27 with total page 327 pages. Available in PDF, EPUB and Kindle. Book excerpt: This second edition of Linear Integral Equations continues the emphasis that the first edition placed on applications. Indeed, many more examples have been added throughout the text. Significant new material has been added in Chapters 6 and 8. For instance, in Chapter 8 we have included the solutions of the Cauchy type integral equations on the real line. Also, there is a section on integral equations with a logarithmic kernel. The bibliography at the end of the book has been exteded and brought up to date. I wish to thank Professor B.K. Sachdeva who has checked the revised man uscript and has suggested many improvements. Last but not least, I am grateful to the editor and staff of Birkhauser for inviting me to prepare this new edition and for their support in preparing it for publication. RamP Kanwal CHAYfERl Introduction 1.1. Definition An integral equation is an equation in which an unknown function appears under one or more integral signs Naturally, in such an equation there can occur other terms as well. For example, for a ~ s ~ b; a :( t :( b, the equations (1.1.1) f(s) = ib K(s, t)g(t)dt, g(s) = f(s) + ib K(s, t)g(t)dt, (1.1.2) g(s) = ib K(s, t)[g(t)fdt, (1.1.3) where the function g(s) is the unknown function and all the other functions are known, are integral equations. These functions may be complex-valued functions of the real variables s and t.

Numerical Methods for the Solution of Ill-Posed Problems

Author : A.N. Tikhonov
Publisher : Springer Science & Business Media
ISBN 13 : 940158480X
Total Pages : 257 pages
Book Rating : 4.4/5 (15 download)

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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.

Analytical and Numerical Methods for Volterra Equations

Author : Peter Linz
Publisher : SIAM
ISBN 13 : 9781611970852
Total Pages : 240 pages
Book Rating : 4.9/5 (78 download)

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Book Synopsis Analytical and Numerical Methods for Volterra Equations by : Peter Linz

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.

Multiscale Methods for Fredholm Integral Equations

Author : Zhongying Chen
Publisher : Cambridge University Press
ISBN 13 : 1107103479
Total Pages : 551 pages
Book Rating : 4.1/5 (71 download)

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Book Synopsis Multiscale Methods for Fredholm Integral Equations by : Zhongying Chen

Download or read book Multiscale Methods for Fredholm Integral Equations written by Zhongying Chen and published by Cambridge University Press. This book was released on 2015-07-16 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.

Computational Methods for Linear Integral Equations

Author : Prem Kythe
Publisher : Springer Science & Business Media
ISBN 13 : 1461201012
Total Pages : 525 pages
Book Rating : 4.4/5 (612 download)

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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.

Newton’s Method: an Updated Approach of Kantorovich’s Theory

Author : José Antonio Ezquerro Fernández
Publisher : Birkhäuser
ISBN 13 : 3319559761
Total Pages : 175 pages
Book Rating : 4.3/5 (195 download)

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Book Synopsis Newton’s Method: an Updated Approach of Kantorovich’s Theory by : José Antonio Ezquerro Fernández

Download or read book Newton’s Method: an Updated Approach of Kantorovich’s Theory written by José Antonio Ezquerro Fernández and published by Birkhäuser. This book was released on 2017-07-05 with total page 175 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows the importance of studying semilocal convergence in iterative methods through Newton's method and addresses the most important aspects of the Kantorovich's theory including implicated studies. Kantorovich's theory for Newton's method used techniques of functional analysis to prove the semilocal convergence of the method by means of the well-known majorant principle. To gain a deeper understanding of these techniques the authors return to the beginning and present a deep-detailed approach of Kantorovich's theory for Newton's method, where they include old results, for a historical perspective and for comparisons with new results, refine old results, and prove their most relevant results, where alternative approaches leading to new sufficient semilocal convergence criteria for Newton's method are given. The book contains many numerical examples involving nonlinear integral equations, two boundary value problems and systems of nonlinear equations related to numerous physical phenomena. The book is addressed to researchers in computational sciences, in general, and in approximation of solutions of nonlinear problems, in particular.

Handbook of Computational Methods for Integration

Author : Prem K. Kythe
Publisher : CRC Press
ISBN 13 : 1135437521
Total Pages : 622 pages
Book Rating : 4.1/5 (354 download)

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Book Synopsis Handbook of Computational Methods for Integration by : Prem K. Kythe

Download or read book Handbook of Computational Methods for Integration written by Prem K. Kythe and published by CRC Press. This book was released on 2004-12-20 with total page 622 pages. Available in PDF, EPUB and Kindle. Book excerpt: During the past 20 years, there has been enormous productivity in theoretical as well as computational integration. Some attempts have been made to find an optimal or best numerical method and related computer code to put to rest the problem of numerical integration, but the research is continuously ongoing, as this problem is still very much open-ended. The importance of numerical integration in so many areas of science and technology has made a practical, up-to-date reference on this subject long overdue. The Handbook of Computational Methods for Integration discusses quadrature rules for finite and infinite range integrals and their applications in differential and integral equations, Fourier integrals and transforms, Hartley transforms, fast Fourier and Hartley transforms, Laplace transforms and wavelets. The practical, applied perspective of this book makes it unique among the many theoretical books on numerical integration and quadrature. It will be a welcomed addition to the libraries of applied mathematicians, scientists, and engineers in virtually every discipline.