Numerical Models For Differential Problems

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Numerical Models For Differential Problems

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2010-01-22

Numerical Models For Differential Problems written by Alfio Quarteroni 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 2010-01-22 with Mathematics categories.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Numerical Models For Differential Problems

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business
Release Date : 2014-04-25

Numerical Models For Differential Problems written by Alfio Quarteroni and has been published by Springer Science & Business this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-04-25 with Mathematics categories.

In this text, we introduce the basic concepts for the numerical modelling of partial differential equations. We consider the classical elliptic, parabolic and hyperbolic linear equations, but also the diffusion, transport, and Navier-Stokes equations, as well as equations representing conservation laws, saddle-point problems and optimal control problems. Furthermore, we provide numerous physical examples which underline such equations. We then analyze numerical solution methods based on finite elements, finite differences, finite volumes, spectral methods and domain decomposition methods, and reduced basis methods. In particular, we discuss the algorithmic and computer implementation aspects and provide a number of easy-to-use programs. The text does not require any previous advanced mathematical knowledge of partial differential equations: the absolutely essential concepts are reported in a preliminary chapter. It is therefore suitable for students of bachelor and master courses in scientific disciplines, and recommendable to those researchers in the academic and extra-academic domain who want to approach this interesting branch of applied mathematics.

Numerical Approximation Of Partial Differential Equations

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Author : Alfio Quarteroni
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-02-11

Numerical Approximation Of Partial Differential Equations written by Alfio Quarteroni 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 2009-02-11 with Mathematics categories.

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).

Numerical Solution Of Initial Value Problems In Differential Algebraic Equations

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Author : K. E. Brenan
language : en
Publisher: SIAM
Release Date : 1996-01-01

Numerical Solution Of Initial Value Problems In Differential Algebraic Equations written by K. E. Brenan and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1996-01-01 with Mathematics categories.

This book describes some of the places where differential-algebraic equations (DAE's) occur.

Numerical Methods For Nonlinear Partial Differential Equations

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Author : Sören Bartels
language : en
Publisher: Springer
Release Date : 2015-01-19

Numerical Methods For Nonlinear Partial Differential Equations written by Sören Bartels and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2015-01-19 with Mathematics categories.

The description of many interesting phenomena in science and engineering leads to infinite-dimensional minimization or evolution problems that define nonlinear partial differential equations. While the development and analysis of numerical methods for linear partial differential equations is nearly complete, only few results are available in the case of nonlinear equations. This monograph devises numerical methods for nonlinear model problems arising in the mathematical description of phase transitions, large bending problems, image processing, and inelastic material behavior. For each of these problems the underlying mathematical model is discussed, the essential analytical properties are explained, and the proposed numerical method is rigorously analyzed. The practicality of the algorithms is illustrated by means of short implementations.

Numerical Methods For Elliptic And Parabolic Partial Differential Equations

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Author : Peter Knabner
language : en
Publisher: Springer Science & Business Media
Release Date : 2003-06-26

Numerical Methods For Elliptic And Parabolic Partial Differential Equations written by Peter Knabner 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 2003-06-26 with Mathematics categories.

This text provides an application oriented introduction to the numerical methods for partial differential equations. It covers finite difference, finite element, and finite volume methods, interweaving theory and applications throughout. The book examines modern topics such as adaptive methods, multilevel methods, and methods for convection-dominated problems and includes detailed illustrations and extensive exercises.

Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations

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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 1988-01-01

Numerical Solution Of Boundary Value Problems For Ordinary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 1988-01-01 with Mathematics categories.

This book is the most comprehensive, up-to-date account of the popular numerical methods for solving boundary value problems in ordinary differential equations. It aims at a thorough understanding of the field by giving an in-depth analysis of the numerical methods by using decoupling principles. Numerous exercises and real-world examples are used throughout to demonstrate the methods and the theory. Although first published in 1988, this republication remains the most comprehensive theoretical coverage of the subject matter, not available elsewhere in one volume. Many problems, arising in a wide variety of application areas, give rise to mathematical models which form boundary value problems for ordinary differential equations. These problems rarely have a closed form solution, and computer simulation is typically used to obtain their approximate solution. This book discusses methods to carry out such computer simulations in a robust, efficient, and reliable manner.

Numerical Methods For Nonlinear Engineering Models

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Author : John R. Hauser
language : en
Publisher: Springer Science & Business Media
Release Date : 2009-03-24

Numerical Methods For Nonlinear Engineering Models written by John R. Hauser 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 2009-03-24 with Technology & Engineering categories.

There are many books on the use of numerical methods for solving engineering problems and for modeling of engineering artifacts. In addition there are many styles of such presentations ranging from books with a major emphasis on theory to books with an emphasis on applications. The purpose of this book is hopefully to present a somewhat different approach to the use of numerical methods for - gineering applications. Engineering models are in general nonlinear models where the response of some appropriate engineering variable depends in a nonlinear manner on the - plication of some independent parameter. It is certainly true that for many types of engineering models it is sufficient to approximate the real physical world by some linear model. However, when engineering environments are pushed to - treme conditions, nonlinear effects are always encountered. It is also such - treme conditions that are of major importance in determining the reliability or failure limits of engineering systems. Hence it is essential than engineers have a toolbox of modeling techniques that can be used to model nonlinear engineering systems. Such a set of basic numerical methods is the topic of this book. For each subject area treated, nonlinear models are incorporated into the discussion from the very beginning and linear models are simply treated as special cases of more general nonlinear models. This is a basic and fundamental difference in this book from most books on numerical methods.

Finite Difference Methods For Ordinary And Partial Differential Equations

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Author : Randall J. LeVeque
language : en
Publisher: SIAM
Release Date : 2007-01-01

Finite Difference Methods For Ordinary And Partial Differential Equations written by Randall J. LeVeque and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2007-01-01 with Mathematics categories.

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.

Numerical Methods For Evolutionary Differential Equations

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Author : Uri M. Ascher
language : en
Publisher: SIAM
Release Date : 2008-09-04

Numerical Methods For Evolutionary Differential Equations written by Uri M. Ascher and has been published by SIAM this book supported file pdf, txt, epub, kindle and other format this book has been release on 2008-09-04 with Mathematics categories.

Develops, analyses, and applies numerical methods for evolutionary, or time-dependent, differential problems.