Download or read book Approximate Solution of Operator Equations written by M.A. Krasnosel'skii and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 495 pages. Available in PDF, EPUB and Kindle. Book excerpt: One of the most important chapters in modern functional analysis is the theory of approximate methods for solution of various mathematical problems. Besides providing considerably simplified approaches to numerical methods, the ideas of functional analysis have also given rise to essentially new computation schemes in problems of linear algebra, differential and integral equations, nonlinear analysis, and so on. The general theory of approximate methods includes many known fundamental results. We refer to the classical work of Kantorovich; the investigations of projection methods by Bogolyubov, Krylov, Keldysh and Petrov, much furthered by Mikhlin and Pol'skii; Tikho nov's methods for approximate solution of ill-posed problems; the general theory of difference schemes; and so on. During the past decade, the Voronezh seminar on functional analysis has systematically discussed various questions related to numerical methods; several advanced courses have been held at Voronezh Uni versity on the application of functional analysis to numerical mathe matics. Some of this research is summarized in the present monograph. The authors' aim has not been to give an exhaustive account, even of the principal known results. The book consists of five chapters.
Download or read book On Galerkin s Method for the Approximate Solution of Linear Operator Equations written by G. R. Richter and published by . This book was released on 1976 with total page 26 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Linear Operator Equations written by M. Thamban Nair and published by World Scientific. This book was released on 2009 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many problems in science and engineering have their mathematical formulation as an operator equation Tx=y, where T is a linear or nonlinear operator between certain function spaces. In practice, such equations are solved approximately using numerical methods, as their exact solution may not often be possible or may not be worth looking for due to physical constraints. In such situations, it is desirable to know how the so-called approximate solution approximates the exact solution, and what the error involved in such procedures would be. This book is concerned with the investigation of the above theoretical issues related to approximately solving linear operator equations. The main tools used for this purpose are basic results from functional analysis and some rudimentary ideas from numerical analysis. To make this book more accessible to readers, no in-depth knowledge on these disciplines is assumed for reading this book.
Download or read book Approximate Solution Of Operator Equations With Applications written by Ioannis K Argyros and published by World Scientific Publishing Company. This book was released on 2005-08-26 with total page 527 pages. Available in PDF, EPUB and Kindle. Book excerpt: Researchers are faced with the problem of solving a variety of equations in the course of their work in engineering, economics, physics, and the computational sciences. This book focuses on a new and improved local-semilocal and monotone convergence analysis of efficient numerical methods for computing approximate solutions of such equations, under weaker hypotheses than in other works. This particular feature is the main strength of the book when compared with others already in the literature.The explanations and applications in the book are detailed enough to capture the interest of curious readers and complete enough to provide the necessary background material to go further into the subject.
Download or read book Optimization of Methods for Approximate Solution of Operator Equations written by Sergei V. Pereverzev and published by Nova Science Publishers. This book was released on 1996 with total page 362 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomee and published by Springer Science & Business Media. This book was released on 2013-04-17 with total page 310 pages. Available in PDF, EPUB and Kindle. Book excerpt: My purpose in this monograph is to present an essentially self-contained account of the mathematical theory of Galerkin finite element methods as applied to parabolic partial differential equations. The emphases and selection of topics reflects my own involvement in the field over the past 25 years, and my ambition has been to stress ideas and methods of analysis rather than to describe the most general and farreaching results possible. Since the formulation and analysis of Galerkin finite element methods for parabolic problems are generally based on ideas and results from the corresponding theory for stationary elliptic problems, such material is often included in the presentation. The basis of this work is my earlier text entitled Galerkin Finite Element Methods for Parabolic Problems, Springer Lecture Notes in Mathematics, No. 1054, from 1984. This has been out of print for several years, and I have felt a need and been encouraged by colleagues and friends to publish an updated version. In doing so I have included most of the contents of the 14 chapters of the earlier work in an updated and revised form, and added four new chapters, on semigroup methods, on multistep schemes, on incomplete iterative solution of the linear algebraic systems at the time levels, and on semilinear equations. The old chapters on fully discrete methods have been reworked by first treating the time discretization of an abstract differential equation in a Hilbert space setting, and the chapter on the discontinuous Galerkin method has been completely rewritten.
Download or read book On the Galerkin Method with Vector Basis Functions written by Hong Zhang Sun and published by . This book was released on 1989 with total page 108 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximate Solutions of Operator Equations written by Mingjun Chen and published by World Scientific. This book was released on 1997 with total page 368 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book offers an elementary and self-contained introduction to many fundamental issues concerning approximate solutions of operator equations formulated in an abstract Banach space setting, including important topics such as solvability, computational schemes, convergence, stability and error estimates. The operator equations under investigation include various linear and nonlinear types of ordinary and partial differential equations, integral equations, and abstract evolution equations, which are frequently involved in applied mathematics and engineering applications.Each chapter contains well-selected examples and exercises, for the purposes of demonstrating the fundamental theories and methods developed in the text and familiarizing the reader with functional analysis techniques useful for numerical solutions of various operator equations.
Download or read book Galerkin Finite Element Methods for Parabolic Problems written by Vidar Thomée and published by Springer Science & Business Media. This book was released on 2010 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximate Solution of Linear Operator Equations written by M. Thamban Nair and published by . This book was released on 1998 with total page 119 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Approximation of Additive Convolution Like Operators written by Victor Didenko and published by Springer Science & Business Media. This book was released on 2008-09-19 with total page 313 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book deals with numerical analysis for certain classes of additive operators and related equations, including singular integral operators with conjugation, the Riemann-Hilbert problem, Mellin operators with conjugation, double layer potential equation, and the Muskhelishvili equation. The authors propose a unified approach to the analysis of the approximation methods under consideration based on special real extensions of complex C*-algebras. The list of the methods considered includes spline Galerkin, spline collocation, qualocation, and quadrature methods. The book is self-contained and accessible to graduate students.
Download or read book Spectral Approximation of Linear Operators written by Francoise Chatelin and published by SIAM. This book was released on 2011-05-26 with total page 482 pages. Available in PDF, EPUB and Kindle. Book excerpt: Originally published: New York: Academic Press, 1983.
Download or read book Methods for Solving Operator Equations written by Vitalij P. Tanana and published by VSP. This book was released on 1997 with total page 236 pages. Available in PDF, EPUB and Kindle. Book excerpt: The Inverse and Ill-Posed Problems Series is a series of monographs publishing postgraduate level information on inverse and ill-posed problems for an international readership of professional scientists and researchers. The series aims to publish works which involve both theory and applications in, e.g., physics, medicine, geophysics, acoustics, electrodynamics, tomography, and ecology.
Download or read book Numerical Solution of Integral Equations written by Michael A. Golberg and published by Springer. This book was released on 1990-06-30 with total page 418 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.
Download or read book Approximate Solution of Operator Equations written by Mark Aleksandrovich Krasnoselʹskiĭ and published by . This book was released on 1969 with total page 484 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Numerical Analysis written by R. Teman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 170 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is an introduction to one of the important as pects of Numerical Analysis, namely the approximate solution of functional equations. We intend to show, by a few brief examples, the different theoretical and practical problems related to the numerical approximation of boundary value problems. We have chosen for this the approximate solution of certain linear elliptic partial differential equations (the first two parts of the book) and the approximate solution of a nonlinear elliptic differential equation. This book is not a systematic study of the subject, but the methods developed here can be applied to large classes of linear and nonlinear elliptic problems. The book assumes that the reader's knowledge of Anal ysis is comparable to what is taught in the first years of graduate studies. This means a good knowledge of Hilbert spaces, elements of measure theory and theory of distributions. The subject matter of the book covers the usual content of a first course on Numerical Analysis of partial differential equations.
Download or read book Integral Equations and Iteration Methods in Electromagnetic Scattering written by A. B. Samokhin and published by Walter de Gruyter. This book was released on 2013-03-12 with total page 112 pages. Available in PDF, EPUB and Kindle. Book excerpt:
