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 Approximate Solutions Of Operator Equations written by Guanrong Chen and published by World Scientific. This book was released on 1997-07-01 with total page 360 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 Approximate Solutions of Integral and Operator Equations written by Philip M. Anselone and published by . This book was released on 1963 with total page 16 pages. Available in PDF, EPUB and Kindle. Book excerpt: The classical method of replacing an integral equation with an algebraic system is considered by means of numerical integration. This is equivalent to replacing the integral operator K with a degenerate operator K sub n acting in the same space. The important properties are that K sub n f approaches Kf for each f, K is compact, and the K sub n are compact in aggregate. (Author).
Download or read book Approximation Methods for Solutions of Differential and Integral Equations written by V. K. Dzyadyk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2018-11-05 with total page 332 pages. Available in PDF, EPUB and Kindle. Book excerpt: No detailed description available for "Approximation Methods for Solutions of Differential and Integral Equations".
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 Wavelet Based Approximation Schemes for Singular Integral Equations written by Madan Mohan Panja and published by CRC Press. This book was released on 2020-06-07 with total page 466 pages. Available in PDF, EPUB and Kindle. Book excerpt: Many mathematical problems in science and engineering are defined by ordinary or partial differential equations with appropriate initial-boundary conditions. Among the various methods, boundary integral equation method (BIEM) is probably the most effective. It’s main advantage is that it changes a problem from its formulation in terms of unbounded differential operator to one for an integral/integro-differential operator, which makes the problem tractable from the analytical or numerical point of view. Basically, the review/study of the problem is shifted to a boundary (a relatively smaller domain), where it gives rise to integral equations defined over a suitable function space. Integral equations with singular kernels areamong the most important classes in the fields of elasticity, fluid mechanics, electromagnetics and other domains in applied science and engineering. With the advancesin computer technology, numerical simulations have become important tools in science and engineering. Several methods have been developed in numerical analysis for equations in mathematical models of applied sciences. Widely used methods include: Finite Difference Method (FDM), Finite Element Method (FEM), Finite Volume Method (FVM) and Galerkin Method (GM). Unfortunately, none of these are versatile. Each has merits and limitations. For example, the widely used FDM and FEM suffers from difficulties in problem solving when rapid changes appear in singularities. Even with the modern computing machines, analysis of shock-wave or crack propagations in three dimensional solids by the existing classical numerical schemes is challenging (computational time/memory requirements). Therefore, with the availability of faster computing machines, research into the development of new efficient schemes for approximate solutions/numerical simulations is an ongoing parallel activity. Numerical methods based on wavelet basis (multiresolution analysis) may be regarded as a confluence of widely used numerical schemes based on Finite Difference Method, Finite Element Method, Galerkin Method, etc. The objective of this monograph is to deal with numerical techniques to obtain (multiscale) approximate solutions in wavelet basis of different types of integral equations with kernels involving varieties of singularities appearing in the field of elasticity, fluid mechanics, electromagnetics and many other domains in applied science and engineering.
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 Random Equations written by Albert T. Bharucha-Reid and published by North-Holland. This book was released on 1979 with total page 264 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book The Theory of Approximate Methods and Their Applications to the Numerical Solution of Singular Integral Equations written by A.A. Ivanov and published by Springer Science & Business Media. This book was released on 1976-06-30 with total page 358 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 The Approximate Solution of Integral Operator Equations Using Complementary Variational Techniques written by A. J. Perks and published by . This book was released on 1979 with total page 104 pages. Available in PDF, EPUB and Kindle. Book excerpt:
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 Collectively Compact Operator Approximation Theory and Applications to Integral Equations written by Philip M. Anselone and published by Prentice Hall. This book was released on 1971 with total page 164 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Convergence Rates of Approximate Least Squares Solutions of Linear Integral and Operator Equations of the First Kind written by M. Zuhair Nashed and published by . This book was released on 1973 with total page 31 pages. Available in PDF, EPUB and Kindle. Book excerpt: The authors consider approximations (x sub n) obtained by moment discretization to (i) the minimal (L sub 2)-norm solution of Kx = y where K is a Hilbert-Schmidt integral operator on (L sub 2), and to (ii) the least squares solution of minimal (L sub 2)-norm of the same equation when y is not in the range R(K) of K. (Modified author abstract).
Download or read book Approximate Methods for Solution of Differential and Integral Equations written by Solomon Grigorʹevich Mikhlin and published by . This book was released on 1967 with total page 328 pages. Available in PDF, EPUB and Kindle. Book excerpt: The aim of this book is to acquaint the reader with the most important and powerful methods of approximate solution of boundary-value problems (including the Cauchy problem) for differential equations, both ordinary and partial, as well as approximate methods for solution of the most frequently encountered types of integral equations: Fredholm, Volterra and singular one-dimensional. This covers the entire domain of classical applications of mathematical analysis to mechanics, engineering, and mathematical physics.
Download or read book Journal of Integral Equations written by and published by . This book was released on 1985 with total page 308 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Download or read book Ill Posed Problems with A Priori Information written by V. V. Vasin and published by Walter de Gruyter. This book was released on 2013-02-18 with total page 268 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.
