Numerical Methods For Elliptic And Parabolic Partial Differential Equations
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Author |
: Peter Knabner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 437 |
Release |
: 2003-06-26 |
ISBN-10 |
: 9780387954493 |
ISBN-13 |
: 038795449X |
Rating |
: 4/5 (93 Downloads) |
Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
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.
Author |
: Peter Knabner |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 437 |
Release |
: 2006-05-26 |
ISBN-10 |
: 9780387217628 |
ISBN-13 |
: 0387217622 |
Rating |
: 4/5 (28 Downloads) |
Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
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.
Author |
: Peter Knabner |
Publisher |
: Springer Nature |
Total Pages |
: 811 |
Release |
: 2021-11-19 |
ISBN-10 |
: 9783030793852 |
ISBN-13 |
: 3030793850 |
Rating |
: 4/5 (52 Downloads) |
Synopsis Numerical Methods for Elliptic and Parabolic Partial Differential Equations by : Peter Knabner
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.
Author |
: John A. Trangenstein |
Publisher |
: Cambridge University Press |
Total Pages |
: 657 |
Release |
: 2013-04-18 |
ISBN-10 |
: 9780521877268 |
ISBN-13 |
: 0521877261 |
Rating |
: 4/5 (68 Downloads) |
Synopsis Numerical Solution of Elliptic and Parabolic Partial Differential Equations with CD-ROM by : John A. Trangenstein
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).
Author |
: Stig Larsson |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 263 |
Release |
: 2008-12-05 |
ISBN-10 |
: 9783540887058 |
ISBN-13 |
: 3540887059 |
Rating |
: 4/5 (58 Downloads) |
Synopsis Partial Differential Equations with Numerical Methods by : Stig Larsson
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.
Author |
: John A. Trangenstein |
Publisher |
: Cambridge University Press |
Total Pages |
: 0 |
Release |
: 2009-09-03 |
ISBN-10 |
: 9780521877275 |
ISBN-13 |
: 052187727X |
Rating |
: 4/5 (75 Downloads) |
Synopsis Numerical Solution of Hyperbolic Partial Differential Equations by : John A. Trangenstein
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.
Author |
: Claes Johnson |
Publisher |
: Courier Corporation |
Total Pages |
: 290 |
Release |
: 2012-05-23 |
ISBN-10 |
: 9780486131597 |
ISBN-13 |
: 0486131599 |
Rating |
: 4/5 (97 Downloads) |
Synopsis Numerical Solution of Partial Differential Equations by the Finite Element Method by : Claes Johnson
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.
Author |
: William F. Ames |
Publisher |
: Academic Press |
Total Pages |
: 380 |
Release |
: 2014-05-10 |
ISBN-10 |
: 9781483262420 |
ISBN-13 |
: 1483262421 |
Rating |
: 4/5 (20 Downloads) |
Synopsis Numerical Methods for Partial Differential Equations by : William F. Ames
Numerical Methods for Partial Differential Equations, Second Edition deals with the use of numerical methods to solve partial differential equations. In addition to numerical fluid mechanics, hopscotch and other explicit-implicit methods are also considered, along with Monte Carlo techniques, lines, fast Fourier transform, and fractional steps methods. Comprised of six chapters, this volume begins with an introduction to numerical calculation, paying particular attention to the classification of equations and physical problems, asymptotics, discrete methods, and dimensionless forms. Subsequent chapters focus on parabolic and hyperbolic equations, elliptic equations, and special topics ranging from singularities and shocks to Navier-Stokes equations and Monte Carlo methods. The final chapter discuss the general concepts of weighted residuals, with emphasis on orthogonal collocation and the Bubnov-Galerkin method. The latter procedure is used to introduce finite elements. This book should be a valuable resource for students and practitioners in the fields of computer science and applied mathematics.
Author |
: Tarek Mathew |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 775 |
Release |
: 2008-06-25 |
ISBN-10 |
: 9783540772095 |
ISBN-13 |
: 354077209X |
Rating |
: 4/5 (95 Downloads) |
Synopsis Domain Decomposition Methods for the Numerical Solution of Partial Differential Equations by : Tarek Mathew
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.
Author |
: Christian Grossmann |
Publisher |
: Springer Science & Business Media |
Total Pages |
: 601 |
Release |
: 2007-08-11 |
ISBN-10 |
: 9783540715849 |
ISBN-13 |
: 3540715843 |
Rating |
: 4/5 (49 Downloads) |
Synopsis Numerical Treatment of Partial Differential Equations by : Christian Grossmann
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.