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Analysis Of Approximation Methods For Differential And Integral Equations
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Author :Hans-Jürgen Reinhardt Publisher :Springer Science & Business Media ISBN 13 :1461210801 Total Pages :412 pages Book Rating :4.4/5 (612 download)
Book Synopsis Analysis of Approximation Methods for Differential and Integral Equations by : Hans-Jürgen Reinhardt
Download or read book Analysis of Approximation Methods for Differential and Integral Equations written by Hans-Jürgen Reinhardt and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 412 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.
Book Synopsis Analysis of Approximation Methods for Differential and Integral Equations by : Hans-Jürgen Reinhardt
Download or read book Analysis of Approximation Methods for Differential and Integral Equations written by Hans-Jürgen Reinhardt and published by Springer. This book was released on 1985-10-07 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is primarily based on the research done by the Numerical Analysis Group at the Goethe-Universitat in Frankfurt/Main, and on material presented in several graduate courses by the author between 1977 and 1981. It is hoped that the text will be useful for graduate students and for scientists interested in studying a fundamental theoretical analysis of numerical methods along with its application to the most diverse classes of differential and integral equations. The text treats numerous methods for approximating solutions of three classes of problems: (elliptic) boundary-value problems, (hyperbolic and parabolic) initial value problems in partial differential equations, and integral equations of the second kind. The aim is to develop a unifying convergence theory, and thereby prove the convergence of, as well as provide error estimates for, the approximations generated by specific numerical methods. The schemes for numerically solving boundary-value problems are additionally divided into the two categories of finite difference methods and of projection methods for approximating their variational formulations.
Book Synopsis Approximation Methods for Solutions of Differential and Integral Equations by : V. K. Dzyadyk
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".
Book Synopsis Numerical Approximation Methods by : Harold Cohen
Download or read book Numerical Approximation Methods written by Harold Cohen and published by Springer Science & Business Media. This book was released on 2011-09-28 with total page 493 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book presents numerical and other approximation techniques for solving various types of mathematical problems that cannot be solved analytically. In addition to well known methods, it contains some non-standard approximation techniques that are now formally collected as well as original methods developed by the author that do not appear in the literature. This book contains an extensive treatment of approximate solutions to various types of integral equations, a topic that is not often discussed in detail. There are detailed analyses of ordinary and partial differential equations and descriptions of methods for estimating the values of integrals that are presented in a level of detail that will suggest techniques that will be useful for developing methods for approximating solutions to problems outside of this text. The book is intended for researchers who must approximate solutions to problems that cannot be solved analytically. It is also appropriate for students taking courses in numerical approximation techniques.
Book Synopsis Approximate Methods for Solution of Differential and Integral Equations by : Solomon Grigorʹevich Mikhlin
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.
Book Synopsis Techniques of Functional Analysis for Differential and Integral Equations by : Paul Sacks
Download or read book Techniques of Functional Analysis for Differential and Integral Equations written by Paul Sacks and published by Academic Press. This book was released on 2017-05-16 with total page 322 pages. Available in PDF, EPUB and Kindle. Book excerpt: Techniques of Functional Analysis for Differential and Integral Equations describes a variety of powerful and modern tools from mathematical analysis, for graduate study and further research in ordinary differential equations, integral equations and partial differential equations. Knowledge of these techniques is particularly useful as preparation for graduate courses and PhD research in differential equations and numerical analysis, and more specialized topics such as fluid dynamics and control theory. Striking a balance between mathematical depth and accessibility, proofs involving more technical aspects of measure and integration theory are avoided, but clear statements and precise alternative references are given . The work provides many examples and exercises drawn from the literature. Provides an introduction to mathematical techniques widely used in applied mathematics and needed for advanced research in ordinary and partial differential equations, integral equations, numerical analysis, fluid dynamics and other areas Establishes the advanced background needed for sophisticated literature review and research in differential equations and integral equations Suitable for use as a textbook for a two semester graduate level course for M.S. and Ph.D. students in Mathematics and Applied Mathematics
Book Synopsis Applied Functional Analysis. Approximation Methods and Computers by : S.S. Kutateladze
Download or read book Applied Functional Analysis. Approximation Methods and Computers written by S.S. Kutateladze and published by CRC Press. This book was released on 2010-12-12 with total page 400 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book contains the most remarkable papers of L.V. Kantorovich in applied and numerical mathematics. It explores the principal directions of Kantorovich's research in approximate methods. The book covers descriptive set theory and functional analysis in semi-ordered vector spaces.
Book Synopsis Solution Methods for Integral Equations by : M. A. Goldberg
Download or read book Solution Methods for Integral Equations written by M. A. Goldberg and published by Springer Science & Business Media. This book was released on 2013-11-21 with total page 350 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Integral Methods in Science and Engineering by : Christian Constanda
Download or read book Integral Methods in Science and Engineering written by Christian Constanda and published by Springer. This book was released on 2019-07-18 with total page 478 pages. Available in PDF, EPUB and Kindle. Book excerpt: This contributed volume contains a collection of articles on state-of-the-art developments on the construction of theoretical integral techniques and their application to specific problems in science and engineering. The chapters in this book are based on talks given at the Fifteenth International Conference on Integral Methods in Science and Engineering, held July 16-20, 2018 at the University of Brighton, UK, and are written by internationally recognized researchers. The topics addressed are wide ranging, and include: Asymptotic analysis Boundary-domain integral equations Viscoplastic fluid flow Stationary waves Interior Neumann shape optimization Self-configuring neural networks This collection will be of interest to researchers in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines and other professionals for whom integration is an essential tool.
Book Synopsis Wavelet Based Approximation Schemes for Singular Integral Equations by : Madan Mohan Panja
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.
Book Synopsis Ordinary Differential Equations and Integral Equations by : C.T.H. Baker
Download or read book Ordinary Differential Equations and Integral Equations written by C.T.H. Baker and published by Elsevier. This book was released on 2001-06-20 with total page 558 pages. Available in PDF, EPUB and Kindle. Book excerpt: /homepage/sac/cam/na2000/index.html7-Volume Set now available at special set price ! This volume contains contributions in the area of differential equations and integral equations. Many numerical methods have arisen in response to the need to solve "real-life" problems in applied mathematics, in particular problems that do not have a closed-form solution. Contributions on both initial-value problems and boundary-value problems in ordinary differential equations appear in this volume. Numerical methods for initial-value problems in ordinary differential equations fall naturally into two classes: those which use one starting value at each step (one-step methods) and those which are based on several values of the solution (multistep methods). John Butcher has supplied an expert's perspective of the development of numerical methods for ordinary differential equations in the 20th century. Rob Corless and Lawrence Shampine talk about established technology, namely software for initial-value problems using Runge-Kutta and Rosenbrock methods, with interpolants to fill in the solution between mesh-points, but the 'slant' is new - based on the question, "How should such software integrate into the current generation of Problem Solving Environments?" Natalia Borovykh and Marc Spijker study the problem of establishing upper bounds for the norm of the nth power of square matrices. The dynamical system viewpoint has been of great benefit to ODE theory and numerical methods. Related is the study of chaotic behaviour. Willy Govaerts discusses the numerical methods for the computation and continuation of equilibria and bifurcation points of equilibria of dynamical systems. Arieh Iserles and Antonella Zanna survey the construction of Runge-Kutta methods which preserve algebraic invariant functions. Valeria Antohe and Ian Gladwell present numerical experiments on solving a Hamiltonian system of Hénon and Heiles with a symplectic and a nonsymplectic method with a variety of precisions and initial conditions. Stiff differential equations first became recognized as special during the 1950s. In 1963 two seminal publications laid to the foundations for later development: Dahlquist's paper on A-stable multistep methods and Butcher's first paper on implicit Runge-Kutta methods. Ernst Hairer and Gerhard Wanner deliver a survey which retraces the discovery of the order stars as well as the principal achievements obtained by that theory. Guido Vanden Berghe, Hans De Meyer, Marnix Van Daele and Tanja Van Hecke construct exponentially fitted Runge-Kutta methods with s stages. Differential-algebraic equations arise in control, in modelling of mechanical systems and in many other fields. Jeff Cash describes a fairly recent class of formulae for the numerical solution of initial-value problems for stiff and differential-algebraic systems. Shengtai Li and Linda Petzold describe methods and software for sensitivity analysis of solutions of DAE initial-value problems. Again in the area of differential-algebraic systems, Neil Biehn, John Betts, Stephen Campbell and William Huffman present current work on mesh adaptation for DAE two-point boundary-value problems. Contrasting approaches to the question of how good an approximation is as a solution of a given equation involve (i) attempting to estimate the actual error (i.e., the difference between the true and the approximate solutions) and (ii) attempting to estimate the defect
Author : Publisher : ISBN 13 :0486821609 Total Pages : pages Book Rating :4.4/5 (868 download)
Book Synopsis Multiscale Methods for Fredholm Integral Equations by : Zhongying Chen
Download or read book Multiscale Methods for Fredholm Integral Equations written by Zhongying Chen and published by Cambridge University Press. This book was released on 2015-07-16 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Presents the state of the art in the study of fast multiscale methods for solving these equations based on wavelets.
Book Synopsis Integral Equations: A Practical Treatment, from Spectral Theory to Applications by : David Porter
Download or read book Integral Equations: A Practical Treatment, from Spectral Theory to Applications written by David Porter and published by Cambridge University Press. This book was released on 1990-09-28 with total page 388 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book gives a rigorous and practical treatment of integral equations. These are significant because they occur in many problems in mathematics, physics and engineering and they offer a powerful (sometimes the only) technique for solving these problems. The book aims to tackle the solution of integral equations using a blend of abstract 'structural' results and more direct, down-to-earth mathematics. The interplay between these two approaches is a central feature of the text and it allows a thorough account to be given of many of the types of integral equation which arise in application areas. Since it is not always possible to find explicit solutions of the problems posed, much attention is devoted to obtaining qualitative information and approximations to the solutions, with the associated error estimates. This treatment is intended for final year mathematics undergraduates, postgraduates and research workers in application areas such as numerical analysis and fluid mechanics.
Book Synopsis Integral Methods in Science and Engineering by : M. Zuhair Nashed
Download or read book Integral Methods in Science and Engineering written by M. Zuhair Nashed and published by Springer Science & Business Media. This book was released on 2006-11-24 with total page 311 pages. Available in PDF, EPUB and Kindle. Book excerpt: The quantitative and qualitative study of the physical world makes use of many mathematical models governed by a great diversity of ordinary, partial differential, integral, and integro-differential equations. An essential step in such investigations is the solution of these types of equations, which sometimes can be performed analytically, while at other times only numerically. This edited, self-contained volume presents a series of state-of-the-art analytic and numerical methods of solution constructed for important problems arising in science and engineering, all based on the powerful operation of (exact or approximate) integration. The volume may be used as a reference guide and a practical resource. It is suitable for researchers and practitioners in applied mathematics, physics, and mechanical and electrical engineering, as well as graduate students in these disciplines.
Book Synopsis Weighted Polynomial Approximation and Numerical Methods for Integral Equations by : Peter Junghanns
Download or read book Weighted Polynomial Approximation and Numerical Methods for Integral Equations written by Peter Junghanns and published by Springer Nature. This book was released on 2021-08-10 with total page 662 pages. Available in PDF, EPUB and Kindle. Book excerpt: 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.
Book Synopsis Periodic Integral and Pseudodifferential Equations with Numerical Approximation by : Jukka Saranen
Download or read book Periodic Integral and Pseudodifferential Equations with Numerical Approximation written by Jukka Saranen and published by Springer Science & Business Media. This book was released on 2013-03-09 with total page 461 pages. Available in PDF, EPUB and Kindle. Book excerpt: An attractive book on the intersection of analysis and numerical analysis, deriving classical boundary integral equations arising from the potential theory and acoustics. This self-contained monograph can be used as a textbook by graduate/postgraduate students. It also contains a lot of carefully chosen exercises.
