A Posteriori Estimates Of Inverse Operators For Initial Value Problems In Linear Ordinary Differential Equations
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A Posteriori Estimates Of Inverse Operators For Initial Value Problems In Linear Ordinary Differential Equations
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Author : Takehiko Kinoshita
language : en
Publisher:
Release Date : 2011
A Posteriori Estimates Of Inverse Operators For Initial Value Problems In Linear Ordinary Differential Equations written by Takehiko Kinoshita and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 2011 with Inverse problems (Differential equations) categories.
Inverse Spectral Problems For Linear Differential Operators And Their Applications
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Author : V A Yurko
language : en
Publisher: CRC Press
Release Date : 2000-01-18
Inverse Spectral Problems For Linear Differential Operators And Their Applications written by V A Yurko and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2000-01-18 with Mathematics categories.
Aims to construct the inverse problem theory for ordinary non-self-adjoint differential operators of arbitary order on the half-line and on a finite interval. The book consists of two parts: in the first part the author presents a general inverse problem of recovering differential equations with integrable coefficients when the behaviour of the spe
Generalized Inverse Operators
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Author : Alexander Andreevych Boichuk
language : en
Publisher: Walter de Gruyter GmbH & Co KG
Release Date : 2016-08-22
Generalized Inverse Operators written by Alexander Andreevych Boichuk and has been published by Walter de Gruyter GmbH & Co KG this book supported file pdf, txt, epub, kindle and other format this book has been release on 2016-08-22 with Mathematics categories.
The book is devoted to the foundations of the theory of boundary-value problems for various classes of systems of differential-operator equations whose linear part is represented by Fredholm operators of the general form. A common point of view on numerous classes of problems that were traditionally studied independently of each other enables us to study, in a natural way, the theory of these problems, to supplement and improve the existing results, and in certain cases, study some of these problems for the first time. With the help of the technique of generalized inverse operators, the Vishik– Lyusternik method, and iterative methods, we perform a detailed investigation of the problems of existence, bifurcations, and branching of the solutions of linear and nonlinear boundary-value problems for various classes of differential-operator systems and propose new procedures for their construction. For more than 11 years that have passed since the appearance of the first edition of the monograph, numerous new publications of the authors in this direction have appeared. In this connection, it became necessary to make some additions and corrections to the previous extensively cited edition, which is still of signifi cant interest for the researchers. For researchers, teachers, post-graduate students, and students of physical and mathematical departments of universities. Contents: Preliminary Information Generalized Inverse Operators in Banach Spaces Pseudoinverse Operators in Hilbert Spaces Boundary-Value Problems for Operator Equations Boundary-Value Problems for Systems of Ordinary Differential Equations Impulsive Boundary-Value Problems for Systems of Ordinary Differential Equations Solutions of Differential and Difference Systems Bounded on the Entire Real Axis
Error Estimation And Iterative Improvement For The Numerical Solution Of Operator Equations
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Author : Bengt Lindberg
language : en
Publisher:
Release Date : 1976
Error Estimation And Iterative Improvement For The Numerical Solution Of Operator Equations written by Bengt Lindberg and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1976 with Differential equations categories.
A Method for estimation of the global discretization error of solutions of operator equations is presented. Further an algorithm for iterative improvement of the approximate solution of such problems is given. The theoretical foudation for the algorithms are given as a number of theorems. Several classes of operator equations are examined and numerical results for both the error estimation algorithm and the algorithm for iterative improvement are given for some classes of ordinary and partial differential equations and integral equations. (Author).
Besov Spaces And Applications To Difference Methods For Initial Value Problems
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Author : P. Brenner
language : en
Publisher: Lecture Notes in Mathematics
Release Date : 1975-02-04
Besov Spaces And Applications To Difference Methods For Initial Value Problems written by P. Brenner and has been published by Lecture Notes in Mathematics this book supported file pdf, txt, epub, kindle and other format this book has been release on 1975-02-04 with Mathematics categories.
Numerical Initial Value Problems In Ordinary Differential Equations
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Author : Charles William Gear
language : en
Publisher: Prentice Hall
Release Date : 1971
Numerical Initial Value Problems In Ordinary Differential Equations written by Charles William Gear and has been published by Prentice Hall this book supported file pdf, txt, epub, kindle and other format this book has been release on 1971 with Mathematics categories.
Introduction -- Higher order one-step methods -- Systems of equations and equations of order greater than one -- Convergence, error bounds, and error estimates for one-step methods -- The choice of step size and order -- Extrapolation methods -- Multivalue or multistep methods - introduction -- General multistep methods, order and stability -- Multivalue methods -- Existence, convergence, and error estimates for multivalue methods -- Special methods for special problems -- Choosing a method.
A Posteriori Error Analysis Via Duality Theory
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Author : Weimin Han
language : en
Publisher: Springer Science & Business Media
Release Date : 2006-07-30
A Posteriori Error Analysis Via Duality Theory written by Weimin Han 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 2006-07-30 with Mathematics categories.
This work provides a posteriori error analysis for mathematical idealizations in modeling boundary value problems, especially those arising in mechanical applications, and for numerical approximations of numerous nonlinear var- tional problems. An error estimate is called a posteriori if the computed solution is used in assessing its accuracy. A posteriori error estimation is central to m- suring, controlling and minimizing errors in modeling and numerical appr- imations. In this book, the main mathematical tool for the developments of a posteriori error estimates is the duality theory of convex analysis, documented in the well-known book by Ekeland and Temam ([49]). The duality theory has been found useful in mathematical programming, mechanics, numerical analysis, etc. The book is divided into six chapters. The first chapter reviews some basic notions and results from functional analysis, boundary value problems, elliptic variational inequalities, and finite element approximations. The most relevant part of the duality theory and convex analysis is briefly reviewed in Chapter 2.
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations
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Author : Mitsuhiro T. Nakao
language : en
Publisher: Springer Nature
Release Date : 2019-11-11
Numerical Verification Methods And Computer Assisted Proofs For Partial Differential Equations written by Mitsuhiro T. Nakao and has been published by Springer Nature this book supported file pdf, txt, epub, kindle and other format this book has been release on 2019-11-11 with Mathematics categories.
In the last decades, various mathematical problems have been solved by computer-assisted proofs, among them the Kepler conjecture, the existence of chaos, the existence of the Lorenz attractor, the famous four-color problem, and more. In many cases, computer-assisted proofs have the remarkable advantage (compared with a “theoretical” proof) of additionally providing accurate quantitative information. The authors have been working more than a quarter century to establish methods for the verified computation of solutions for partial differential equations, mainly for nonlinear elliptic problems of the form -∆u=f(x,u,∇u) with Dirichlet boundary conditions. Here, by “verified computation” is meant a computer-assisted numerical approach for proving the existence of a solution in a close and explicit neighborhood of an approximate solution. The quantitative information provided by these techniques is also significant from the viewpoint of a posteriori error estimates for approximate solutions of the concerned partial differential equations in a mathematically rigorous sense. In this monograph, the authors give a detailed description of the verified computations and computer-assisted proofs for partial differential equations that they developed. In Part I, the methods mainly studied by the authors Nakao and Watanabe are presented. These methods are based on a finite dimensional projection and constructive a priori error estimates for finite element approximations of the Poisson equation. In Part II, the computer-assisted approaches via eigenvalue bounds developed by the author Plum are explained in detail. The main task of this method consists of establishing eigenvalue bounds for the linearization of the corresponding nonlinear problem at the computed approximate solution. Some brief remarks on other approaches are also given in Part III. Each method in Parts I and II is accompanied by appropriate numerical examples that confirm the actual usefulness of the authors’ methods. Also in some examples practical computer algorithms are supplied so that readers can easily implement the verification programs by themselves.
A Posteriori Error Estimation Techniques For Finite Element Methods
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Author : Rüdiger Verfürth
language : en
Publisher: OUP Oxford
Release Date : 2013-04-18
A Posteriori Error Estimation Techniques For Finite Element Methods written by Rüdiger Verfürth and has been published by OUP Oxford this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-04-18 with Mathematics categories.
Self-adaptive discretization methods are now an indispensable tool for the numerical solution of partial differential equations that arise from physical and technical applications. The aim is to obtain a numerical solution within a prescribed tolerance using a minimal amount of work. The main tools in achieving this goal are a posteriori error estimates which give global and local information on the error of the numerical solution and which can easily be computed from the given numerical solution and the data of the differential equation. This book reviews the most frequently used a posteriori error estimation techniques and applies them to a broad class of linear and nonlinear elliptic and parabolic equations. Although there are various approaches to adaptivity and a posteriori error estimation, they are all based on a few common principles. The main aim of the book is to elaborate these basic principles and to give guidelines for developing adaptive schemes for new problems. Chapters 1 and 2 are quite elementary and present various error indicators and their use for mesh adaptation in the framework of a simple model problem. The basic principles are introduced using a minimal amount of notations and techniques providing a complete overview for the non-specialist. Chapters 4-6 on the other hand are more advanced and present a posteriori error estimates within a general framework using the technical tools collected in Chapter 3. Most sections close with a bibliographical remark which indicates the historical development and hints at further results.
Surveys On Solution Methods For Inverse Problems
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Author : David Colton
language : en
Publisher: Springer Science & Business Media
Release Date : 2012-12-06
Surveys On Solution Methods For Inverse Problems written by David Colton 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 2012-12-06 with Mathematics categories.
Inverse problems are concerned with determining causes for observed or desired effects. Problems of this type appear in many application fields both in science and in engineering. The mathematical modelling of inverse problems usually leads to ill-posed problems, i.e., problems where solutions need not exist, need not be unique or may depend discontinuously on the data. For this reason, numerical methods for solving inverse problems are especially difficult, special methods have to be developed which are known under the term "regularization methods". This volume contains twelve survey papers about solution methods for inverse and ill-posed problems and about their application to specific types of inverse problems, e.g., in scattering theory, in tomography and medical applications, in geophysics and in image processing. The papers have been written by leading experts in the field and provide an up-to-date account of solution methods for inverse problems.