Numerical Methods for Elliptic and Parabolic Partial Differential Equations

Numerical Methods for Elliptic and Parabolic Partial Differential Equations
Title Numerical Methods for Elliptic and Parabolic Partial Differential Equations PDF eBook
Author Peter Knabner
Publisher Springer Science & Business Media
Pages 437
Release 2003-06-26
Genre Mathematics
ISBN 038795449X

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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 Elliptic and Parabolic Partial Differential Equations with CD-ROM

Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM
Title Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM PDF eBook
Author John A. Trangenstein
Publisher Cambridge University Press
Pages 657
Release 2013-04-18
Genre Mathematics
ISBN 0521877261

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For mathematicians and engineers interested in applying numerical methods to physical problems this book is ideal. Numerical ideas are connected to accompanying software, which is also available online. By seeing the complete description of the methods in both theory and implementation, students will more easily gain the knowledge needed to write their own application programs or develop new theory. The book contains careful development of the mathematical tools needed for analysis of the numerical methods, including elliptic regularity theory and approximation theory. Variational crimes, due to quadrature, coordinate mappings, domain approximation and boundary conditions, are analyzed. The claims are stated with full statement of the assumptions and conclusions, and use subscripted constants which can be traced back to the origination (particularly in the electronic version, which can be found on the accompanying CD-ROM).

Partial Differential Equations with Numerical Methods

Partial Differential Equations with Numerical Methods
Title Partial Differential Equations with Numerical Methods PDF eBook
Author Stig Larsson
Publisher Springer Science & Business Media
Pages 263
Release 2008-12-05
Genre Mathematics
ISBN 3540887059

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The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix. The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering.

Numerical Solution of Hyperbolic Partial Differential Equations

Numerical Solution of Hyperbolic Partial Differential Equations
Title Numerical Solution of Hyperbolic Partial Differential Equations PDF eBook
Author John A. Trangenstein
Publisher Cambridge University Press
Pages 0
Release 2009-09-03
Genre Mathematics
ISBN 052187727X

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Numerical Solution of Hyperbolic Partial Differential Equations is a new type of graduate textbook, with both print and interactive electronic components (on CD). It is a comprehensive presentation of modern shock-capturing methods, including both finite volume and finite element methods, covering the theory of hyperbolic conservation laws and the theory of the numerical methods. The range of applications is broad enough to engage most engineering disciplines and many areas of applied mathematics. Classical techniques for judging the qualitative performance of the schemes are used to motivate the development of classical higher-order methods. The interactive CD gives access to the computer code used to create all of the text's figures, and lets readers run simulations, choosing their own input parameters; the CD displays the results of the experiments as movies. Consequently, students can gain an appreciation for both the dynamics of the problem application, and the growth of numerical errors.

Numerical Solution of Partial Differential Equations by the Finite Element Method

Numerical Solution of Partial Differential Equations by the Finite Element Method
Title Numerical Solution of Partial Differential Equations by the Finite Element Method PDF eBook
Author Claes Johnson
Publisher Courier Corporation
Pages 290
Release 2012-05-23
Genre Mathematics
ISBN 0486131599

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An accessible introduction to the finite element method for solving numeric problems, this volume offers the keys to an important technique in computational mathematics. Suitable for advanced undergraduate and graduate courses, it outlines clear connections with applications and considers numerous examples from a variety of science- and engineering-related specialties.This text encompasses all varieties of the basic linear partial differential equations, including elliptic, parabolic and hyperbolic problems, as well as stationary and time-dependent problems. Additional topics include finite element methods for integral equations, an introduction to nonlinear problems, and considerations of unique developments of finite element techniques related to parabolic problems, including methods for automatic time step control. The relevant mathematics are expressed in non-technical terms whenever possible, in the interests of keeping the treatment accessible to a majority of students.

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations

Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations
Title Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations PDF eBook
Author Tarek Mathew
Publisher Springer Science & Business Media
Pages 775
Release 2008-06-25
Genre Mathematics
ISBN 354077209X

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Domain decomposition methods are divide and conquer computational methods for the parallel solution of partial differential equations of elliptic or parabolic type. The methodology includes iterative algorithms, and techniques for non-matching grid discretizations and heterogeneous approximations. This book serves as a matrix oriented introduction to domain decomposition methodology. A wide range of topics are discussed include hybrid formulations, Schwarz, and many more.

Numerical Treatment of Partial Differential Equations

Numerical Treatment of Partial Differential Equations
Title Numerical Treatment of Partial Differential Equations PDF eBook
Author Christian Grossmann
Publisher Springer Science & Business Media
Pages 601
Release 2007-08-11
Genre Mathematics
ISBN 3540715843

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This book deals with discretization techniques for partial differential equations of elliptic, parabolic and hyperbolic type. It provides an introduction to the main principles of discretization and gives a presentation of the ideas and analysis of advanced numerical methods in the area. The book is mainly dedicated to finite element methods, but it also discusses difference methods and finite volume techniques. Coverage offers analytical tools, properties of discretization techniques and hints to algorithmic aspects. It also guides readers to current developments in research.