Computational Methods For Linear Integral Equations

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Computational Methods for Linear Integral Equations

Author : Prem Kythe
Publisher : Springer Science & Business Media
ISBN 13 : 9780817641924
Total Pages : 530 pages
Book Rating : 4.6/5 (419 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 2002-04-26 with total page 530 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.

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.

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.

Constructive and Computational Methods for Differential and Integral Equations

Author : D. L. Colton
Publisher :
ISBN 13 : 9783662206225
Total Pages : 492 pages
Book Rating : 4.2/5 (62 download)

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Book Synopsis Constructive and Computational Methods for Differential and Integral Equations by : D. L. Colton

Download or read book Constructive and Computational Methods for Differential and Integral Equations written by D. L. Colton and published by . This book was released on 2014-09-01 with total page 492 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Linear Integral Equations

Author : William Vernon Lovitt
Publisher :
ISBN 13 :
Total Pages : 280 pages
Book Rating : 4.3/5 (91 download)

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Book Synopsis Linear Integral Equations by : William Vernon Lovitt

Download or read book Linear Integral Equations written by William Vernon Lovitt and published by . This book was released on 1924 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Constructive and Computational Methods for Differential and Integral Equations

Author : D.L. Colton
Publisher : Springer
ISBN 13 : 3540373020
Total Pages : 488 pages
Book Rating : 4.5/5 (43 download)

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Book Synopsis Constructive and Computational Methods for Differential and Integral Equations by : D.L. Colton

Download or read book Constructive and Computational Methods for Differential and Integral Equations written by D.L. Colton and published by Springer. This book was released on 2006-11-15 with total page 488 pages. Available in PDF, EPUB and Kindle. Book excerpt:

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.

Mathematical and Computational Methods for Modelling, Approximation and Simulation

Author : Domingo Barrera
Publisher : Springer Nature
ISBN 13 : 3030943399
Total Pages : 261 pages
Book Rating : 4.0/5 (39 download)

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Book Synopsis Mathematical and Computational Methods for Modelling, Approximation and Simulation by : Domingo Barrera

Download or read book Mathematical and Computational Methods for Modelling, Approximation and Simulation written by Domingo Barrera and published by Springer Nature. This book was released on 2022-05-08 with total page 261 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains plenary lectures given at the International Conference on Mathematical and Computational Modeling, Approximation and Simulation, dealing with three very different problems: reduction of Runge and Gibbs phenomena, difficulties arising when studying models that depend on the highly nonlinear behaviour of a system of PDEs, and data fitting with truncated hierarchical B-splines for the adaptive reconstruction of industrial models. The book includes nine contributions, mostly related to quasi-interpolation. This is a topic that continues to register a high level of interest, both for those working in the field of approximation theory and for those interested in its use in a practical context. Two chapters address the construction of quasi-interpolants, and three others focus on the use of quasi-interpolation in solving integral equations. The remaining four concern a problem related to the heat diffusion equation, new results on the notion of convexity in probabilistic metric spaces (which are applied to the study of the existence and uniqueness of the solution of a Volterra equation), the use of smoothing splines to address an economic problem and, finally, the analysis of poverty measures, which is a topic of increased interest to society. The book is addressed to researchers interested in Applied Mathematics, with particular reference to the aforementioned topics.

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.

Integral Equations

Author : Wolfgang Hackbusch
Publisher : Birkhäuser
ISBN 13 : 3034892152
Total Pages : 377 pages
Book Rating : 4.0/5 (348 download)

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Book Synopsis Integral Equations by : Wolfgang Hackbusch

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.

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.

Integral Equation Methods for Electromagnetic and Elastic Waves

Author : Weng Cho Chew
Publisher : Morgan & Claypool Publishers
ISBN 13 : 1598291483
Total Pages : 259 pages
Book Rating : 4.5/5 (982 download)

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Book Synopsis Integral Equation Methods for Electromagnetic and Elastic Waves by : Weng Cho Chew

Download or read book Integral Equation Methods for Electromagnetic and Elastic Waves written by Weng Cho Chew and published by Morgan & Claypool Publishers. This book was released on 2009 with total page 259 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral Equation Methods for Electromagnetic and Elastic Waves is an outgrowth of several years of work. There have been no recent books on integral equation methods. There are books written on integral equations, but either they have been around for a while, or they were written by mathematicians. Much of the knowledge in integral equation methods still resides in journal papers. With this book, important relevant knowledge for integral equations are consolidated in one place and researchers need only read the pertinent chapters in this book to gain important knowledge needed for integral equation research. Also, learning the fundamentals of linear elastic wave theory does not require a quantum leap for electromagnetic practitioners. Integral equation methods have been around for several decades, and their introduction to electromagnetics has been due to the seminal works of Richmond and Harrington in the 1960s. There was a surge in the interest in this topic in the 1980s (notably the work of Wilton and his coworkers) due to increased computing power. The interest in this area was on the wane when it was demonstrated that differential equation methods, with their sparse matrices, can solve many problems more efficiently than integral equation methods. Recently, due to the advent of fast algorithms, there has been a revival in integral equation methods in electromagnetics. Much of our work in recent years has been in fast algorithms for integral equations, which prompted our interest in integral equation methods. While previously, only tens of thousands of unknowns could be solved by integral equation methods, now, tens of millions of unknowns can be solved with fast algorithms. This has prompted new enthusiasm in integral equation methods. Table of Contents: Introduction to Computational Electromagnetics / Linear Vector Space, Reciprocity, and Energy Conservation / Introduction to Integral Equations / Integral Equations for Penetrable Objects / Low-Frequency Problems in Integral Equations / Dyadic Green's Function for Layered Media and Integral Equations / Fast Inhomogeneous Plane Wave Algorithm for Layered Media / Electromagnetic Wave versus Elastic Wave / Glossary of Acronyms

Solution Methods for Integral Equations

Author : M. A. Goldberg
Publisher : Springer Science & Business Media
ISBN 13 : 1475714661
Total Pages : 351 pages
Book Rating : 4.4/5 (757 download)

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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:

Computational Methods for Integral Equations

Author : Saeed Vahdati
Publisher :
ISBN 13 : 9783659186400
Total Pages : 0 pages
Book Rating : 4.1/5 (864 download)

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Book Synopsis Computational Methods for Integral Equations by : Saeed Vahdati

Download or read book Computational Methods for Integral Equations written by Saeed Vahdati and published by . This book was released on 2012-09-25 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Computational Methods for Solving System of Volterra Integral Equation

Author : Rostam K. Saeed
Publisher : LAP Lambert Academic Publishing
ISBN 13 : 9783844330755
Total Pages : 164 pages
Book Rating : 4.3/5 (37 download)

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Book Synopsis Computational Methods for Solving System of Volterra Integral Equation by : Rostam K. Saeed

Download or read book Computational Methods for Solving System of Volterra Integral Equation written by Rostam K. Saeed and published by LAP Lambert Academic Publishing. This book was released on 2011-04 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt: In this work the existence and uniqueness theorem for single linear Volterra integral equation has been generalized to a system of linear Volterra integral equation of the second kind. Depending on Banach fixed point theorem, some new results have been proved.Also, a Taylor series expansion has been considered to solve a system of linear Volterra integral equations of the second kind and a system of linear Volterra integro-differential equations of the second kind.In addition, three different types of iterative methods have been formulated to solve above systems. Furthermore, we derive a new iterative method named by "modified successive approximation method" to solve above systems. By this modification a faster rate of convergence for the successive method is established. Also, we proved a new theorem about the existence, uniqueness and convergence of this method. Two different kinds of weighted residual methods have been applied to treat the above systems. Moreover, the spectral method has been modified and applied for solving the above systems.

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

Integral Equations and Their Applications

Author : Matiur Rahman
Publisher : WIT Press
ISBN 13 : 1845641019
Total Pages : 385 pages
Book Rating : 4.8/5 (456 download)

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Book Synopsis Integral Equations and Their Applications by : Matiur Rahman

Download or read book Integral Equations and Their Applications written by Matiur Rahman and published by WIT Press. This book was released on 2007 with total page 385 pages. Available in PDF, EPUB and Kindle. Book excerpt: The book deals with linear integral equations, that is, equations involving an unknown function which appears under the integral sign and contains topics such as Abel's integral equation, Volterra integral equations, Fredholm integral integral equations, singular and nonlinear integral equations, orthogonal systems of functions, Green's function as a symmetric kernel of the integral equations.