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The Method Of Differential Approximation
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Book Synopsis The Method of Differential Approximation by : Y.I. Shokin
Download or read book The Method of Differential Approximation written by Y.I. Shokin and published by Springer. This book was released on 1983-05 with total page 320 pages. Available in PDF, EPUB and Kindle. Book excerpt: I am very glad that this book is now accessible to English-speaking scientists. During the three years following the publication of the original Russian edition, the method of differential approximation has been rapidly expanded and unfortunately I was unable to incorporate into the English edition all of the material which whould have reflected its present state of development. Nevertheless, a considerable amount of recently obtained results have been added and the bibliography has been enlarged accordingly, so that the English edition is one third longer than the Russian original. Mathematical rigorousness is a basic feature of this monograph. The reader should therefore be familiar with the theory of partial differential equations and difference equations. Some knowledge of group theory as applied to problems in physics, especially the theory of Lie groups, would also be useful. The treatment of the approximation of gas dynamic equations focuses on the question of how to characterize the typical features of difference equations on the basis of the related differential approximation, which can be discussed using the fully developed theory of partial differential equations.
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 The Method of Differential Approximation by : Y.I. Shokin
Download or read book The Method of Differential Approximation written by Y.I. Shokin and published by Springer. This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt: I am very glad that this book is now accessible to English-speaking scientists. During the three years following the publication of the original Russian edition, the method of differential approximation has been rapidly expanded and unfortunately I was unable to incorporate into the English edition all of the material which whould have reflected its present state of development. Nevertheless, a considerable amount of recently obtained results have been added and the bibliography has been enlarged accordingly, so that the English edition is one third longer than the Russian original. Mathematical rigorousness is a basic feature of this monograph. The reader should therefore be familiar with the theory of partial differential equations and difference equations. Some knowledge of group theory as applied to problems in physics, especially the theory of Lie groups, would also be useful. The treatment of the approximation of gas dynamic equations focuses on the question of how to characterize the typical features of difference equations on the basis of the related differential approximation, which can be discussed using the fully developed theory of partial differential equations.
Book Synopsis Numerical Approximation of Partial Differential Equations by : Alfio Quarteroni
Download or read book Numerical Approximation of Partial Differential Equations written by Alfio Quarteroni and published by Springer Science & Business Media. This book was released on 2009-02-11 with total page 551 pages. Available in PDF, EPUB and Kindle. Book excerpt: Everything is more simple than one thinks but at the same time more complex than one can understand Johann Wolfgang von Goethe To reach the point that is unknown to you, you must take the road that is unknown to you St. John of the Cross This is a book on the numerical approximation ofpartial differential equations (PDEs). Its scope is to provide a thorough illustration of numerical methods (especially those stemming from the variational formulation of PDEs), carry out their stability and convergence analysis, derive error bounds, and discuss the algorithmic aspects relative to their implementation. A sound balancing of theoretical analysis, description of algorithms and discussion of applications is our primary concern. Many kinds of problems are addressed: linear and nonlinear, steady and time-dependent, having either smooth or non-smooth solutions. Besides model equations, we consider a number of (initial-) boundary value problems of interest in several fields of applications. Part I is devoted to the description and analysis of general numerical methods for the discretization of partial differential equations. A comprehensive theory of Galerkin methods and its variants (Petrov Galerkin and generalized Galerkin), as wellas ofcollocationmethods, is devel oped for the spatial discretization. This theory is then specified to two numer ical subspace realizations of remarkable interest: the finite element method (conforming, non-conforming, mixed, hybrid) and the spectral method (Leg endre and Chebyshev expansion).
Book Synopsis The Method of Differential Approximation by : I︠U︡riĭ Ivanovich Shokin
Download or read book The Method of Differential Approximation written by I︠U︡riĭ Ivanovich Shokin and published by Springer Verlag. This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Numerical Approximation of Partial Differential Equations by : Sören Bartels
Download or read book Numerical Approximation of Partial Differential Equations written by Sören Bartels and published by Springer. This book was released on 2016-06-02 with total page 541 pages. Available in PDF, EPUB and Kindle. Book excerpt: Finite element methods for approximating partial differential equations have reached a high degree of maturity, and are an indispensible tool in science and technology. This textbook aims at providing a thorough introduction to the construction, analysis, and implementation of finite element methods for model problems arising in continuum mechanics. The first part of the book discusses elementary properties of linear partial differential equations along with their basic numerical approximation, the functional-analytical framework for rigorously establishing existence of solutions, and the construction and analysis of basic finite element methods. The second part is devoted to the optimal adaptive approximation of singularities and the fast iterative solution of linear systems of equations arising from finite element discretizations. In the third part, the mathematical framework for analyzing and discretizing saddle-point problems is formulated, corresponding finte element methods are analyzed, and particular applications including incompressible elasticity, thin elastic objects, electromagnetism, and fluid mechanics are addressed. The book includes theoretical problems and practical projects for all chapters, and an introduction to the implementation of finite element methods.
Book Synopsis Polynomial Approximation of Differential Equations by : Daniele Funaro
Download or read book Polynomial Approximation of Differential Equations written by Daniele Funaro and published by Springer Science & Business Media. This book was released on 2008-10-04 with total page 315 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the analysis of approximate solution techniques for differential equations, based on classical orthogonal polynomials. These techniques are popularly known as spectral methods. In the last few decades, there has been a growing interest in this subject. As a matter offact, spectral methods provide a competitive alternative to other standard approximation techniques, for a large variety of problems. Initial ap plications were concerned with the investigation of periodic solutions of boundary value problems using trigonometric polynomials. Subsequently, the analysis was extended to algebraic polynomials. Expansions in orthogonal basis functions were preferred, due to their high accuracy and flexibility in computations. The aim of this book is to present a preliminary mathematical background for be ginners who wish to study and perform numerical experiments, or who wish to improve their skill in order to tackle more specific applications. In addition, it furnishes a com prehensive collection of basic formulas and theorems that are useful for implementations at any level of complexity. We tried to maintain an elementary exposition so that no experience in functional analysis is required.
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 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 Partial Differential Equations: Modeling, Analysis and Numerical Approximation by : Hervé Le Dret
Download or read book Partial Differential Equations: Modeling, Analysis and Numerical Approximation written by Hervé Le Dret and published by Birkhäuser. This book was released on 2016-02-11 with total page 403 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book is devoted to the study of partial differential equation problems both from the theoretical and numerical points of view. After presenting modeling aspects, it develops the theoretical analysis of partial differential equation problems for the three main classes of partial differential equations: elliptic, parabolic and hyperbolic. Several numerical approximation methods adapted to each of these examples are analyzed: finite difference, finite element and finite volumes methods, and they are illustrated using numerical simulation results. Although parts of the book are accessible to Bachelor students in mathematics or engineering, it is primarily aimed at Masters students in applied mathematics or computational engineering. The emphasis is on mathematical detail and rigor for the analysis of both continuous and discrete problems.
Book Synopsis Finite Difference Methods for Ordinary and Partial Differential Equations by : Randall J. LeVeque
Download or read book Finite Difference Methods for Ordinary and Partial Differential Equations written by Randall J. LeVeque and published by SIAM. This book was released on 2007-01-01 with total page 356 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book introduces finite difference methods for both ordinary differential equations (ODEs) and partial differential equations (PDEs) and discusses the similarities and differences between algorithm design and stability analysis for different types of equations. A unified view of stability theory for ODEs and PDEs is presented, and the interplay between ODE and PDE analysis is stressed. The text emphasizes standard classical methods, but several newer approaches also are introduced and are described in the context of simple motivating examples.
Book Synopsis Approximation Methods in Science and Engineering by : Reza N. Jazar
Download or read book Approximation Methods in Science and Engineering written by Reza N. Jazar and published by . This book was released on 2020 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximation Methods in Engineering and Science covers fundamental and advanced topics in three areas: Dimensional Analysis, Continued Fractions, and Stability Analysis of the Mathieu Differential Equation. Throughout the book, a strong emphasis is given to concepts and methods used in everyday calculations. Dimensional analysis is a crucial need for every engineer and scientist to be able to do experiments on scaled models and use the results in real world applications. Knowing that most nonlinear equations have no analytic solution, the power series solution is assumed to be the first approach to derive an approximate solution. However, this book will show the advantages of continued fractions and provides a systematic method to develop better approximate solutions in continued fractions. It also shows the importance of determining stability chart of the Mathieu equation and reviews and compares several approximate methods for that. The book provides the energy-rate method to study the stability of parametric differential equations that generates much better approximate solutions. Covers practical model-prototype analysis and nondimensionalization of differential equations; Coverage includes approximate methods of responses of nonlinear differential equations; Discusses how to apply approximation methods to analysis, design, optimization, and control problems; Discusses how to implement approximation methods to new aspects of engineering and physics including nonlinear vibration and vehicle dynamics
Book Synopsis The Method of Differential Approximation by : Yurii Ivanovich Shokin
Download or read book The Method of Differential Approximation written by Yurii Ivanovich Shokin and published by . This book was released on 1983 with total page 0 pages. Available in PDF, EPUB and Kindle. Book excerpt:
Book Synopsis Introduction to Numerical Methods in Differential Equations by : Mark H. Holmes
Download or read book Introduction to Numerical Methods in Differential Equations written by Mark H. Holmes and published by Springer Science & Business Media. This book was released on 2007-04-05 with total page 248 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book shows how to derive, test and analyze numerical methods for solving differential equations, including both ordinary and partial differential equations. The objective is that students learn to solve differential equations numerically and understand the mathematical and computational issues that arise when this is done. Includes an extensive collection of exercises, which develop both the analytical and computational aspects of the material. In addition to more than 100 illustrations, the book includes a large collection of supplemental material: exercise sets, MATLAB computer codes for both student and instructor, lecture slides and movies.
Book Synopsis Approximate Analytical Methods for Solving Ordinary Differential Equations by : T.S.L Radhika
Download or read book Approximate Analytical Methods for Solving Ordinary Differential Equations written by T.S.L Radhika and published by CRC Press. This book was released on 2014-11-21 with total page 200 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approximate Analytical Methods for Solving Ordinary Differential Equations (ODEs) is the first book to present all of the available approximate methods for solving ODEs, eliminating the need to wade through multiple books and articles. It covers both well-established techniques and recently developed procedures, including the classical series solut
Book Synopsis Methods in Approximation by : N.D. Bellman
Download or read book Methods in Approximation written by N.D. Bellman and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 239 pages. Available in PDF, EPUB and Kindle. Book excerpt: Approach your problems from the right end It isn't that they can't see the solution. It is and begin with the answers. Then one day, that they can't see the problem. perhaps you will find the final question. G. K. Chesterton. The Scandal of Father 'The Hermit Clad in Crane Feathers' in R. Brown 'The point of a Pin'. van Gulik's The Chinese Maze Murders. Growing specialization and diversification have brought a host of monographs and textbooks on increasingly specialized topics. However, the "tree" of knowledge of mathematics and related fields does not grow only by putting forth new branches. It also happens, quite often in fact, that branches which were thought to be completely disparate are suddenly seen to be related. Further, the kind and level of sophistication of mathematics applied in various sciences has changed drastically in recent years: measure theory is used (non trivially) in regional and theoretical economics; algebraic geometry interacts with physics; the Minkowsky lemma, coding theory and the structure of water meet one another in packing and covering theory; quantum fields, crystal defects and mathematical programming profit from homotopy theory; Lie algebras are relevant to filtering; and prediction and electrical engineering can use Stein spaces. And in addition to this there are such new emerging subdisciplines as "experimental mathematics", "CFD", "completely integrable systems", "chaos, synergetics and large-scale order", which are almost impossible to fit into the existing classification schemes. They draw upon widely different sections of mathematics.
Book Synopsis Convergence, Approximation, and Differential Equations by : Eugene A. Herman
Download or read book Convergence, Approximation, and Differential Equations written by Eugene A. Herman and published by John Wiley & Sons. This book was released on 1986 with total page 408 pages. Available in PDF, EPUB and Kindle. Book excerpt: A new approach to the teaching of undergraduate level mathematics that includes topics from numerical analysis, calculus and differential equations. It stresses a modern viewpoint, combining both computational and theoretical aspects that will help students use the computer as a daily tool as well as aid them in the understanding of basic theoretical concepts. Numerous examples, applications and exercise sets are also included in the text.
