Novel Methods For Solving Linear And Nonlinear Integral Equations

Author : Santanu Saha Ray
Publisher : CRC Press
ISBN 13 : 042977737X
Total Pages : 242 pages
Book Rating : 4.70/5 ( download)

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Download or read book Novel Methods for Solving Linear and Nonlinear Integral Equations written by Santanu Saha Ray and published by CRC Press. This book was released on 2018-12-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

Author : Abdul-Majid Wazwaz
Publisher : Springer Science & Business Media
ISBN 13 : 3642214495
Total Pages : 639 pages
Book Rating : 4.93/5 ( download)

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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 : Santanu Saha Ray
Publisher : CRC Press
ISBN 13 : 0429777388
Total Pages : 242 pages
Book Rating : 4.87/5 ( download)

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Download or read book Novel Methods for Solving Linear and Nonlinear Integral Equations written by Santanu Saha Ray and published by CRC Press. This book was released on 2018-12-07 with total page 242 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with the numerical solution of integral equations based on approximation of functions and the authors apply wavelet approximation to the unknown function of integral equations. The book's goal is to categorize the selected methods and assess their accuracy and efficiency.

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 0203881052
Total Pages : 1143 pages
Book Rating : 4.57/5 ( download)

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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

Author : Harold Thayer Davis
Publisher :
ISBN 13 :
Total Pages : 590 pages
Book Rating : 4.0I/5 ( download)

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Download or read book Introduction to Nonlinear Differential and Integral Equations written by Harold Thayer Davis and published by . This book was released on 1960 with total page 590 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Author : R Precup
Publisher : Springer Science & Business Media
ISBN 13 : 9401599866
Total Pages : 221 pages
Book Rating : 4.63/5 ( download)

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Download or read book Methods in Nonlinear Integral Equations written by R Precup and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 221 pages. Available in PDF, EPUB and Kindle. Book excerpt: Methods in Nonlinear Integral Equations presents several extremely fruitful methods for the analysis of systems and nonlinear integral equations. They include: fixed point methods (the Schauder and Leray-Schauder principles), variational methods (direct variational methods and mountain pass theorems), and iterative methods (the discrete continuation principle, upper and lower solutions techniques, Newton's method and the generalized quasilinearization method). Many important applications for several classes of integral equations and, in particular, for initial and boundary value problems, are presented to complement the theory. Special attention is paid to the existence and localization of solutions in bounded domains such as balls and order intervals. The presentation is essentially self-contained and leads the reader from classical concepts to current ideas and methods of nonlinear analysis.

Author : Ram P. Kanwal
Publisher : Springer Science & Business Media
ISBN 13 : 1461207657
Total Pages : 327 pages
Book Rating : 4.58/5 ( download)

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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.

Author : Juan R. Torregrosa
Publisher : MDPI
ISBN 13 : 3039219405
Total Pages : 494 pages
Book Rating : 4.07/5 ( download)

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Download or read book Iterative Methods for Solving Nonlinear Equations and Systems written by Juan R. Torregrosa and published by MDPI. This book was released on 2019-12-06 with total page 494 pages. Available in PDF, EPUB and Kindle. Book excerpt: Solving nonlinear equations in Banach spaces (real or complex nonlinear equations, nonlinear systems, and nonlinear matrix equations, among others), is a non-trivial task that involves many areas of science and technology. Usually the solution is not directly affordable and require an approach using iterative algorithms. This Special Issue focuses mainly on the design, analysis of convergence, and stability of new schemes for solving nonlinear problems and their application to practical problems. Included papers study the following topics: Methods for finding simple or multiple roots either with or without derivatives, iterative methods for approximating different generalized inverses, real or complex dynamics associated to the rational functions resulting from the application of an iterative method on a polynomial. Additionally, the analysis of the convergence has been carried out by means of different sufficient conditions assuring the local, semilocal, or global convergence. This Special issue has allowed us to present the latest research results in the area of iterative processes for solving nonlinear equations as well as systems and matrix equations. In addition to the theoretical papers, several manuscripts on signal processing, nonlinear integral equations, or partial differential equations, reveal the connection between iterative methods and other branches of science and engineering.

Author : Andrei D. Polyanin
Publisher : CRC Press
ISBN 13 : 9780849328763
Total Pages : 816 pages
Book Rating : 4.64/5 ( download)

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Download or read book Handbook of Integral Equations written by Andrei D. Polyanin and published by CRC Press. This book was released on 1998-03-31 with total page 816 pages. Available in PDF, EPUB and Kindle. Book excerpt: Integral equations are encountered in various fields of science and in numerous applications, including elasticity, plasticity, heat and mass transfer, oscillation theory, fluid dynamics, filtration theory, electrostatics, electrodynamics, biomechanics, game theory, control, queuing theory, electrical engineering, economics, and medicine. Exact (closed-form) solutions of integral equations play an important role in the proper understanding of qualitative features of many phenomena and processes in various areas of natural science. Equations of physics, chemistry, and biology contain functions or parameters obtained from experiments - hence, they are not strictly fixed. Therefore, it is expedient to choose the structure of these functions for more easily analyzing and solving the equation. As a possible selection criterion, one may adopt the requirement that the model integral equation admit a solution in a closed form. Exact solutions can be used to verify the consistency and estimate errors of various numerical, asymptotic, and approximate methods. The first part of Handbook of Integral Equations: Contains more than 2,100 integral equations and their solutions Includes many new exact solutions to linear and nonlinear equations Addresses equations of general form, which depend on arbitrary functions Other equations contain one or more free parameters (the book actually deals with families of integral equations); the reader has the option to fix these parameters. The second part of the book - chapters 7 through 14 - presents exact, approximate analytical, and numerical methods for solving linear and nonlinear integral equations. Apart from the classical methods, the text also describes some new methods. When selecting the material, the authors emphasize practical aspects of the matter, specifically for methods that allow an effective "constructing" of the solution. Each section provides examples of applicatio

Author : Michael A. Golberg
Publisher : Springer Science & Business Media
ISBN 13 : 1489925937
Total Pages : 428 pages
Book Rating : 4.30/5 ( download)

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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.