Search Results for "computational-partial-differential-equations"

Computational Partial Differential Equations Using MATLAB

• Author: Jichun Li,Yi-Tung Chen
• Publisher: CRC Press
• ISBN: 9781420089059
• Category: Mathematics
• Page: 378
• View: 8441
This textbook introduces several major numerical methods for solving various partial differential equations (PDEs) in science and engineering, including elliptic, parabolic, and hyperbolic equations. It covers traditional techniques that include the classic finite difference method and the finite element method as well as state-of-the-art numerical methods, such as the high-order compact difference method and the radial basis function meshless method. Helps Students Better Understand Numerical Methods through Use of MATLAB® The authors uniquely emphasize both theoretical numerical analysis and practical implementation of the algorithms in MATLAB, making the book useful for students in computational science and engineering. They provide students with simple, clear implementations instead of sophisticated usages of MATLAB functions. All the Material Needed for a Numerical Analysis Course Based on the authors’ own courses, the text only requires some knowledge of computer programming, advanced calculus, and difference equations. It includes practical examples, exercises, references, and problems, along with a solutions manual for qualifying instructors. Students can download MATLAB code from www.crcpress.com, enabling them to easily modify or improve the codes to solve their own problems.

Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

• Author: Hans Petter Langtangen
• Publisher: Springer Science & Business Media
• ISBN: 3662011700
• Category: Mathematics
• Page: 685
• View: 7199
Targeted at students and researchers in computational sciences who need to develop computer codes for solving PDEs, the exposition here is focused on numerics and software related to mathematical models in solid and fluid mechanics. The book teaches finite element methods, and basic finite difference methods from a computational point of view, with the main emphasis on developing flexible computer programs, using the numerical library Diffpack. Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. All the program examples, as well as Diffpack for use with this book, are available on the Internet. XXXXXXX NEUER TEXT This book is for researchers who need to develop computer code for solving PDEs. Numerical methods and the application of Diffpack are explained in detail. Diffpack is a modern C++ development environment that is widely used by industrial scientists and engineers working in areas such as oil exploration, groundwater modeling, and materials testing. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

Advanced Topics in Computational Partial Differential Equations

Numerical Methods and Diffpack Programming

• Author: Hans Petter Langtangen,Aslak Tveito
• Publisher: Springer Science & Business Media
• ISBN: 3642182372
• Category: Mathematics
• Page: 663
• View: 8936
A gentle introduction to advanced topics such as parallel computing, multigrid methods, and special methods for systems of PDEs. The goal of all chapters is to ‘compute’ solutions to problems, hence algorithmic and software issues play a central role. All software examples use the Diffpack programming environment - some experience with Diffpack is required. There are also some chapters covering complete applications, i.e., the way from a model, expressed as systems of PDEs, through to discretization methods, algorithms, software design, verification, and computational examples. Suitable for readers with a background in basic finite element and finite difference methods for partial differential equations.

Computational Methods for PDE in Mechanics

• Author: Berardino D'Acunto
• Publisher: World Scientific
• ISBN: 9789812560377
• Category: Science
• Page: 278
• View: 8972
- An application-oriented introduction to computational numerical methods for PDE - Complete with numerous exercise sets and solutions - Includes Windows programs in C++ language

Adaptive Computational Methods for Partial Differential Equations

• Author: Ivo Babushka,Jagdish Chandra,Joseph E. Flaherty
• Publisher: SIAM
• ISBN: 9780898711912
• Category: Mathematics
• Page: 251
• View: 8768
List of participants; Elliptic equations; Parabolic equations; Hyperbolic equations.

Partial Differential Equations for Computational Science

With Maple and Vector Analysis

• Author: David Betounes
• Publisher: Springer Science & Business Media
• ISBN: 9780387983004
• Category: Mathematics
• Page: 517
• View: 2365
This book will have strong appeal to interdisciplinary audiences, particularly in regard to its treatments of fluid mechanics, heat equations, and continuum mechanics. There is also a heavy focus on vector analysis. Maple examples, exercises, and an appendix is also included.

Introduction to Partial Differential Equations

A Computational Approach

• Author: Aslak Tveito,Ragnar Winther
• Publisher: Springer Science & Business Media
• ISBN: 0387227733
• Category: Mathematics
• Page: 392
• View: 1071
Combining both the classical theory and numerical techniques for partial differential equations, this thoroughly modern approach shows the significance of computations in PDEs and illustrates the strong interaction between mathematical theory and the development of numerical methods. Great care has been taken throughout the book to seek a sound balance between these techniques. The authors present the material at an easy pace and exercises ranging from the straightforward to the challenging have been included. In addition there are some "projects" suggested, either to refresh the students memory of results needed in this course, or to extend the theories developed in the text. Suitable for undergraduate and graduate students in mathematics and engineering.

Computational Optimization of Systems Governed by Partial Differential Equations

• Author: Alfio Borzi,Volker Schulz
• Publisher: SIAM
• ISBN: 1611972043
• Category: Mathematics
• Page: 282
• View: 4461
This book provides a bridge between continuous optimization and PDE modelling and focuses on the numerical solution of the corresponding problems. Intended for graduate students in PDE-constrained optimization, it is also suitable as an introduction for researchers in scientific computing or optimization.

Computational Methods in Partial Differential Equations

• Author: Andrew R. Mitchell,Andrew Ronald Mitchell
• Publisher: John Wiley & Sons
• ISBN: N.A
• Category: Differential equations, Partial
• Page: 255
• View: 5932
October 2002

Partielle Differentialgleichungen und numerische Methoden

• Publisher: Springer-Verlag
• ISBN: 3540274227
• Category: Mathematics
• Page: 272
• View: 8680
Das Buch ist für Studenten der angewandten Mathematik und der Ingenieurwissenschaften auf Vordiplomniveau geeignet. Der Schwerpunkt liegt auf der Verbindung der Theorie linearer partieller Differentialgleichungen mit der Theorie finiter Differenzenverfahren und der Theorie der Methoden finiter Elemente. Für jede Klasse partieller Differentialgleichungen, d.h. elliptische, parabolische und hyperbolische, enthält der Text jeweils ein Kapitel zur mathematischen Theorie der Differentialgleichung gefolgt von einem Kapitel zu finiten Differenzenverfahren sowie einem zu Methoden der finiten Elemente. Den Kapiteln zu elliptischen Gleichungen geht ein Kapitel zum Zweipunkt-Randwertproblem für gewöhnliche Differentialgleichungen voran. Ebenso ist den Kapiteln zu zeitabhängigen Problemen ein Kapitel zum Anfangswertproblem für gewöhnliche Differentialgleichungen vorangestellt. Zudem gibt es ein Kapitel zum elliptischen Eigenwertproblem und zur Entwicklung nach Eigenfunktionen. Die Darstellung setzt keine tiefer gehenden Kenntnisse in Analysis und Funktionalanalysis voraus. Das erforderliche Grundwissen über lineare Funktionalanalysis und Sobolev-Räume wird im Anhang im Überblick besprochen.

Numerische Behandlung partieller Differentialgleichungen

• Author: Christian Großmann,Hans-Görg Roos
• Publisher: Springer-Verlag
• ISBN: 9783519220893
• Category: Mathematics
• Page: 572
• View: 9931
Mathematiker, Naturwissenschaftler und Ingenieure erhalten mit diesem Lehrbuch eine Einführung in die numerische Behandlung partieller Differentialgleichungen. Diskutiert werden die grundlegenden Verfahren - Finite Differenzen, Finite Volumen und Finite Elemente - für die wesentlichen Typen partieller Differentialgleichungen: elliptische, parabolische und hyperbolische Gleichungen. Einbezogen werden auch moderne Methoden zur Lösung der diskreten Probleme. Hinweise auf aktuelle Software sowie zahlreiche Beispiele und Übungsaufgaben runden diese Einführung ab.

The Numerical Solution of Ordinary and Partial Differential Equations

• Author: Granville Sewell
• Publisher: World Scientific
• ISBN: 9814635111
• Category: Mathematics
• Page: 348
• View: 5935

Numerical Partial Differential Equations: Finite Difference Methods

• Author: J.W. Thomas
• Publisher: Springer Science & Business Media
• ISBN: 1489972781
• Category: Mathematics
• Page: 437
• View: 4617
What makes this book stand out from the competition is that it is more computational. Once done with both volumes, readers will have the tools to attack a wider variety of problems than those worked out in the competitors' books. The author stresses the use of technology throughout the text, allowing students to utilize it as much as possible.

Computational Methods for Partial Differential Equations

• Author: E. H. Twizell
• Publisher: Ellis Horwood
• ISBN: N.A
• Category: Differential equations, Partial
• Page: 276
• View: 5428

Partial Differential Equations with Numerical Methods

• Publisher: Springer Science & Business Media
• ISBN: 3540887059
• Category: Mathematics
• Page: 262
• View: 3115
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.

The finite difference method in partial differential equations

• Author: Andrew R. Mitchell,David Francis Griffiths
• Publisher: John Wiley & Sons Inc
• ISBN: N.A
• Category: Mathematics
• Page: 272
• View: 4732
Extensively revised edition of Computational Methods in Partial Differential Equations. A more general approach has been adopted for the splitting of operators for parabolic and hyperbolic equations to include Richtmyer and Strang type splittings in addition to alternating direction implicit and locally one dimensional methods. A description of the now standard factorization and SOR/ADI iterative techniques for solving elliptic difference equations has been supplemented with an account or preconditioned conjugate gradient methods which are currently gaining in popularity. Prominence is also given to the Galerkin method using different test and trial functions as a means of constructing difference approximations to both elliptic and time dependent problems. The applications of finite difference methods have been revised and contain examples involving the treatment of singularities in elliptic equations, free and moving boundary problems, as well as modern developments in computational fluid dynamics. Emphasis throughout is on clear exposition of the construction and solution of difference equations. Material is reinforced with theoretical results when appropriate.

Essential Partial Differential Equations

Analytical and Computational Aspects

• Author: David F. Griffiths,John W. Dold,David J. Silvester
• Publisher: Springer
• ISBN: 3319225693
• Category: Mathematics
• Page: 368
• View: 6837