Computational Methods For Linear Integral Equations

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Computational Methods For Linear Integral Equations

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Author : Prem Kythe
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-06-28

Computational Methods For Linear Integral Equations written by Prem Kythe and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-06-28 with Mathematics categories.

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

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Author : L. M. Delves
language : en
Publisher: CUP Archive
Release Date : 1985

Computational Methods For Integral Equations written by L. M. Delves and has been published by CUP Archive this book supported file pdf, txt, epub, kindle and other format this book has been release on 1985 with Mathematics categories.

This textbook provides a readable account of techniques for numerical solutions.

Handbook Of Computational Methods For Integration

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Author : Prem K. Kythe
language : en
Publisher: CRC Press
Release Date : 2004-12-20

Handbook Of Computational Methods For Integration written by Prem K. Kythe and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2004-12-20 with Mathematics categories.

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.

Linear And Nonlinear Integral Equations

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Author : Abdul-Majid Wazwaz
language : en
Publisher: Springer Science & Business Media
Release Date : 2011-11-24

Linear And Nonlinear Integral Equations written by Abdul-Majid Wazwaz and has been published by Springer Science & Business Media this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-11-24 with Mathematics categories.

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.

Weighted Polynomial Approximation And Numerical Methods For Integral Equations

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Author : Peter Junghanns
language : en
Publisher: Springer Nature
Release Date : 2021-08-10

Weighted Polynomial Approximation And Numerical Methods For Integral Equations written by Peter Junghanns and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2021-08-10 with Mathematics categories.

The book presents a combination of two topics: one coming from the theory of approximation of functions and integrals by interpolation and quadrature, respectively, and the other from the numerical analysis of operator equations, in particular, of integral and related equations. The text focusses on interpolation and quadrature processes for functions defined on bounded and unbounded intervals and having certain singularities at the endpoints of the interval, as well as on numerical methods for Fredholm integral equations of first and second kind with smooth and weakly singular kernel functions, linear and nonlinear Cauchy singular integral equations, and hypersingular integral equations. The book includes both classic and very recent results and will appeal to graduate students and researchers who want to learn about the approximation of functions and the numerical solution of operator equations, in particular integral equations.

Computational Methods For Solving System Of Volterra Integral Equation

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Author : Rostam K. Saeed
language : en
Publisher: LAP Lambert Academic Publishing
Release Date : 2011-04

Computational Methods For Solving System Of Volterra Integral Equation written by Rostam K. Saeed and has been published by LAP Lambert Academic Publishing this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011-04 with categories.

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.

Constructive And Computational Methods For Differential And Integral Equations

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Author : D.L. Colton
language : en
Publisher: Springer
Release Date : 2006-11-15

Constructive And Computational Methods For Differential And Integral Equations written by D.L. Colton and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2006-11-15 with Mathematics categories.

Introduction To Integral Equations With Applications

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Author : Abdul J. Jerri
language : en
Publisher: John Wiley & Sons
Release Date : 1999-09-03

Introduction To Integral Equations With Applications written by Abdul J. Jerri and has been published by John Wiley & Sons this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999-09-03 with Mathematics categories.

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.

Computational Methods For Integral Equations

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Author : Saeed Vahdati
language : en
Publisher:
Release Date : 2012-09-25

Computational Methods For Integral Equations written by Saeed Vahdati and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2012-09-25 with categories.

The Numerical Solution Of Integral Equations Of The Second Kind

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Author : Kendall E. Atkinson
language : en
Publisher: Cambridge University Press
Release Date : 1997-06-28

The Numerical Solution Of Integral Equations Of The Second Kind written by Kendall E. Atkinson and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-06-28 with Mathematics categories.

This book provides an extensive introduction to the numerical solution of a large class of integral equations.