Download or read book Discretization in Differential Equations and Enclosures written by Ernst Adams and published by . This book was released on 1987 with total page 266 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Analysis of Discretization Methods for Ordinary Differential Equations written by Hans J. Stetter and published by Springer Science & Business Media. This book was released on 2013-03-12 with total page 407 pages. Available in PDF, EPUB and Kindle. Book excerpt: Due to the fundamental role of differential equations in science and engineering it has long been a basic task of numerical analysts to generate numerical values of solutions to differential equations. Nearly all approaches to this task involve a "finitization" of the original differential equation problem, usually by a projection into a finite-dimensional space. By far the most popular of these finitization processes consists of a reduction to a difference equation problem for functions which take values only on a grid of argument points. Although some of these finite difference methods have been known for a long time, their wide applica bility and great efficiency came to light only with the spread of electronic computers. This in tum strongly stimulated research on the properties and practical use of finite-difference methods. While the theory or partial differential equations and their discrete analogues is a very hard subject, and progress is consequently slow, the initial value problem for a system of first order ordinary differential equations lends itself so naturally to discretization that hundreds of numerical analysts have felt inspired to invent an ever-increasing number of finite-difference methods for its solution. For about 15 years, there has hardly been an issue of a numerical journal without new results of this kind; but clearly the vast majority of these methods have just been variations of a few basic themes. In this situation, the classical text book by P.

Download or read book The Method of Discretization in Time and Partial Differential Equations written by K. Rektorys and published by Springer. This book was released on 1982-12-31 with total page 454 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Discretization Methods and Iterative Solvers Based on Domain Decomposition written by Barbara I. Wohlmuth and published by Springer Science & Business Media. This book was released on 2012-12-06 with total page 209 pages. Available in PDF, EPUB and Kindle. Book excerpt: Domain decomposition methods provide powerful and flexible tools for the numerical approximation of partial differential equations arising in the modeling of many interesting applications in science and engineering. This book deals with discretization techniques on non-matching triangulations and iterative solvers with particular emphasis on mortar finite elements, Schwarz methods and multigrid techniques. New results on non-standard situations as mortar methods based on dual basis functions and vector field discretizations are analyzed and illustrated by numerical results. The role of trace theorems, harmonic extensions, dual norms and weak interface conditions is emphasized. Although the original idea was used successfully more than a hundred years ago, these methods are relatively new for the numerical approximation. The possibilites of high performance computations and the interest in large- scale problems have led to an increased research activity.

Download or read book Discretization strategies for optimal control problems with parabolic partial differential equations written by Thomas Gerhard Flaig and published by . This book was released on 2013 with total page 148 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Mimetic Discretization Methods written by Jose E. Castillo and published by CRC Press. This book was released on 2013-01-10 with total page 256 pages. Available in PDF, EPUB and Kindle. Book excerpt: To help solve physical and engineering problems, mimetic or compatible algebraic discretization methods employ discrete constructs to mimic the continuous identities and theorems found in vector calculus. Mimetic Discretization Methods focuses on the recent mimetic discretization method co-developed by the first author. Based on the Castillo-Grone operators, this simple mimetic discretization method is invariably valid for spatial dimensions no greater than three. The book also presents a numerical method for obtaining corresponding discrete operators that mimic the continuum differential and flux-integral operators, enabling the same order of accuracy in the interior as well as the domain boundary. After an overview of various mimetic approaches and applications, the text discusses the use of continuum mathematical models as a way to motivate the natural use of mimetic methods. The authors also offer basic numerical analysis material, making the book suitable for a course on numerical methods for solving PDEs. The authors cover mimetic differential operators in one, two, and three dimensions and provide a thorough introduction to object-oriented programming and C++. In addition, they describe how their mimetic methods toolkit (MTK)-available online-can be used for the computational implementation of mimetic discretization methods. The text concludes with the application of mimetic methods to structured nonuniform meshes as well as several case studies. Compiling the authors' many concepts and results developed over the years, this book shows how to obtain a robust numerical solution of PDEs using the mimetic discretization approach. It also helps readers compare alternative methods in the literature.

Download or read book The Gradient Discretisation Method written by Jérôme Droniou and published by Springer. This book was released on 2018-07-31 with total page 501 pages. Available in PDF, EPUB and Kindle. Book excerpt: This monograph presents the Gradient Discretisation Method (GDM), which is a unified convergence analysis framework for numerical methods for elliptic and parabolic partial differential equations. The results obtained by the GDM cover both stationary and transient models; error estimates are provided for linear (and some non-linear) equations, and convergence is established for a wide range of fully non-linear models (e.g. Leray–Lions equations and degenerate parabolic equations such as the Stefan or Richards models). The GDM applies to a diverse range of methods, both classical (conforming, non-conforming, mixed finite elements, discontinuous Galerkin) and modern (mimetic finite differences, hybrid and mixed finite volume, MPFA-O finite volume), some of which can be built on very general meshes.span style="" ms="" mincho";mso-bidi-font-family:="" the="" core="" properties="" and="" analytical="" tools="" required="" to="" work="" within="" gdm="" are="" stressed,="" it="" is="" shown="" that="" scheme="" convergence="" can="" often="" be="" established="" by="" verifying="" a="" small="" number="" of="" properties.="" scope="" some="" featured="" techniques="" results,="" such="" as="" time-space="" compactness="" theorems="" (discrete="" aubin–simon,="" discontinuous="" ascoli–arzela),="" goes="" beyond="" gdm,="" making="" them="" potentially="" applicable="" numerical="" schemes="" not="" (yet)="" known="" fit="" into="" this="" framework.span style="font-family:" ms="" mincho";mso-bidi-font-family:="" this="" monograph="" is="" intended="" for="" graduate="" students,="" researchers="" and="" experts="" in="" the="" field="" of="" numerical="" analysis="" partial="" differential="" equations./ppiiiiibr/i/i/i/i/i/p

Download or read book Survey of Applicable Mathematics written by K. Rektorys and published by Springer. This book was released on 2013-12-19 with total page 1781 pages. Available in PDF, EPUB and Kindle. Book excerpt: This major two-volume handbook is an extensively revised, updated second edition of the highly praised Survey of Applicable Mathematics, first published in English in 1969. The thirty-seven chapters cover all the important mathematical fields of use in applications: algebra, geometry, differential and integral calculus, infinite series, orthogonal systems of functions, Fourier series, special functions, ordinary differential equations, partial differential equations, integral equations, functions of one and several complex variables, conformal mapping, integral transforms, functional analysis, numerical methods in algebra and in algebra and in differential boundary value problems, probability, statistics, stochastic processes, calculus of variations, and linear programming. All proofs have been omitted. However, theorems are carefully formulated, and where considered useful, are commented with explanatory remarks. Many practical examples are given by way of illustration. Each of the two volumes contains an extensive bibliography and a comprehensive index. Together these two volumes represent a survey library of mathematics which is applicable in many fields of science, engineering, economics, etc. For researchers, students and teachers of mathematics and its applications.

Download or read book Fluid Mechanics Aspects of Fire and Smoke Dynamics in Enclosures written by Bart Merci and published by CRC Press. This book was released on 2022-10-24 with total page 424 pages. Available in PDF, EPUB and Kindle. Book excerpt: This book provides essential understanding of flows in fire and smoke dynamics in enclosures, covering combustion, heat transfer and fire suppression in more detail than other introductory books. It moves from the basic equations for turbulent flows with combustion, through a discussion of the structure of flames, to fire and smoke plumes and their interaction with enclosure boundaries. This is then applied to fire dynamics and smoke and heat control in enclosures. This new edition provides considerably more on the fluid mechanics of the effect of water, and on fire dynamics modelling using Computational Fluid Dynamics. Presents worked examples taken from practical, everyday fire-related problems Covers a broad range of topics, from the basics to state-of-the-art computer simulations of fire and smoke-related fluid mechanics, including the effect of water Provides extensive treatment of the interaction of water sprays with a fire-driven flow Contains a chapter on Computational Fluid Dynamics, the increasingly popular calculation method in the field of fire safety science The book serves as a comprehensive guide at the undergraduate and starting researcher level on fire and smoke dynamics in enclosures, with an emphasis on fluid mechanics.

Download or read book Discretization Methods for Neutral Ordinary Differential Equations written by Cyro Patarra and published by . This book was released on 1974 with total page pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book The Problem of Integrable Discretization written by Yuri B. Suris and published by Springer Science & Business Media. This book was released on 2003-06-20 with total page 1118 pages. Available in PDF, EPUB and Kindle. Book excerpt: An exploration of the theory of discrete integrable systems, with an emphasis on the following general problem: how to discretize one or several of independent variables in a given integrable system of differential equations, maintaining the integrability property? This question (related in spirit to such a modern branch of numerical analysis as geometric integration) is treated in the book as an immanent part of the theory of integrable systems, also commonly termed as the theory of solitons. Most of the results are only available from recent journal publications, many of them are new. Thus, the book is a kind of encyclopedia on discrete integrable systems. It unifies the features of a research monograph and a handbook. It is supplied with an extensive bibliography and detailed bibliographic remarks at the end of each chapter. Largely self-contained, it will be accessible to graduate and post-graduate students as well as to researchers in the area of integrable dynamical systems.

Download or read book Systems Analysis and Simulation 1988 I Theory and Foundations Proceedings of the International Symposium held in Berlin GDR September 12 16 1988 written by Achim Sydow and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 428 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Numerical Solution of Differential Equations written by Isaac Fried and published by Academic Press. This book was released on 2014-05-10 with total page 280 pages. Available in PDF, EPUB and Kindle. Book excerpt: Numerical Solution of Differential Equations is a 10-chapter text that provides the numerical solution and practical aspects of differential equations. After a brief overview of the fundamentals of differential equations, this book goes on presenting the principal useful discretization techniques and their theoretical aspects, along with geometrical and physical examples, mainly from continuum mechanics. Considerable chapters are devoted to the development of the techniques of the numerical solution of differential equations and their analysis. The remaining chapters explore the influential invention in computational mechanics-finite elements. Each chapter emphasizes the relationship among the analytic formulation of the physical event, the discretization techniques applied to it, the algebraic properties of the discrete systems created, and the properties of the digital computer. This book will be of great value to undergraduate and graduate mathematics and physics students.

Download or read book Factorization of Measurable Matrix Functions written by G. S. Litvinchuk and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 376 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Advances in Mathematical Optimization written by J. Guddat et al. and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 240 pages. Available in PDF, EPUB and Kindle. Book excerpt:

Download or read book Recent Progress in Multivariate Approximation written by Werner Haussmann and published by Birkhäuser. This book was released on 2012-12-06 with total page 258 pages. Available in PDF, EPUB and Kindle. Book excerpt: Nineteen contributions cover recent topics in constructive approximation on varieties, approximation by solutions of partial differential equations, application of Riesz bases and frames, multiwavelets and subdivision. An essential resource for researchers and graduates in applied mathematics, computer science and geophysics who are interested in the state-of-the-art developments in multivariate approximation.

Download or read book Andreotti Grauert Theory by Integral Formulas written by G. M. Henkin and published by Walter de Gruyter GmbH & Co KG. This book was released on 2022-01-19 with total page 272 pages. Available in PDF, EPUB and Kindle. Book excerpt: