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Computational Partial Differential Equations (Lecture Notes in Computational Science and Engineering) [Hardcover]

H.P. Langtangen
2.0 out of 5 stars  See all reviews (1 customer review)

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Hardcover, Jun 1999 --  
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Book Description

Jun 1999 3540652744 978-3540652748
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.

Product details

  • Hardcover: 705 pages
  • Publisher: Springer-Verlag Berlin and Heidelberg GmbH & Co. K (Jun 1999)
  • Language: English
  • ISBN-10: 3540652744
  • ISBN-13: 978-3540652748
  • Product Dimensions: 23.9 x 16 x 3.3 cm
  • Average Customer Review: 2.0 out of 5 stars  See all reviews (1 customer review)
  • Amazon Bestsellers Rank: 5,818,256 in Books (See Top 100 in Books)
  • See Complete Table of Contents

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Review

From the reviews of the second edition:

"The aim of this book, as stated in the preface is ‘To Teach Numerics along with Diffpack’. … I feel that the author has been successful with the stated aim, and the content is well directed to the target audience … . This book will be very useful … for graduate students or researchers, who intend working with DIFFPACK. It provides an excellent advanced tutorial and users manual for DIFFPACK, while also providing a wealth of first hand computational experience presented by an excellent computational scientist." (Stephen Roberts, gazette The Australian Mathematical Society, Vol. 32 (5), 2005)

"The present book can be considered to be a sort of handbook for Diffpack, yet it is more than just that. … No one planning to use Diffpack is likely not to benefit from this presentation." (H. Muthsam, Monatshefte für Mathematik, Vol. 143 (4), 2004)

"The present version improves and corrects the text, adds new material, and updates the book to match the version 4.0 of the C++ software package Diffpack. … this is a very useful book for the users of Diffpack. However, this book deserves a wider readership than the users of Diffpack, because it provides valuable insights of object oriented numerics and state-of-the-art program development using standard tools for numerical programming, data visualization, and scripting techniques based on Perl." (Matti Vuorinen, Zentralblatt MATH, Vol. 1037 (12), 2004)

"This large monograph … is devoted to an updated presentation of the most important numerical techniques for solving partial differential equations using the software Diffpack Programming. … Many figures and tables make explanation much more easier, in addition a collection of examples are discussed with many details. … In addition a complete bibliography and full index is added. In conclusion this book will be certainly very helpful to everybody involving in numerical simulations and having Diffpack software." (Stéphane Métens, Physicalia, Vol. 26 (1), 2004)

"This is the second edition of a popular tutorial on the numerical solution of partial differential equations (PDEs). … has over 150 exercises and a comparable number of worked-out examples together with computational code. There is an extensive bibliography of 156 references for further reading. … it should be of interest and use to researchers and practitioners working in computational mechanics and to students aspiring to enter that field. It should make a good text for graduate-level numeric courses. Purchase by libraries is recommended." (RL Huston, Applied Mechanics Reviews, Vol. 56 (6), 2003)

--This text refers to an alternate Hardcover edition.

From the Publisher

A CSE book on the industrial mathematics software Diffpack
The target audience of this book is students and researchers in computational sciences who need to develop computer codes for solving partial differential equations. The exposition 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. The main emphasis regards development of flexible computer programs, using the numerical library Diffpack. The application of Diffpack is explained in detail for problems including model equations in applied mathematics, heat transfer, elasticity, and viscous fluid flow. Diffpack is a modern software development environment based on C++ and object-oriented programming. All the program examples, as well as a test version of Diffpack, are available for free over the Internet.

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Diffpack [35] is a sophisticated tool for developing numerical software, with main emphasis on numerical solution of partial differential equations. Read the first page
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Most Helpful Customer Reviews
2.0 out of 5 stars Read once. Think hard while you read. 15 Nov 2001
Format:Hardcover
The book consists of several refined lecture notes of varying quality. The knowledge is there, but it's sometimes hard to extract.
Do not work as a reference for numerical methods. Do not work as a manual for diffpack (a numerical software library). Nevertheless, its probably the best source of diffpack examples.
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Amazon.com: 4.5 out of 5 stars  2 reviews
6 of 6 people found the following review helpful
4.0 out of 5 stars learn C++ via the book's examples 6 July 2008
By W Boudville - Published on Amazon.com
Format:Hardcover
In a way, the book is a throwback to a time when most people learning Fortran were not computer programmers per se, but scientists and engineers who needed to solve some problem using computers. In Langtangen's book, the language of choice is C++. A good choice, given that this edition came out in 2003. C++ has one main advantage over Fortran, in its object oriented ability. The procedural aspect of Fortran has trouble scaling to very large code bodies. However, Langtangen is quick to point out that if you take the time to learn C++ via the book, the coding experience is easily transferred to other languages like Java or even Fortran.

He directs the book towards a student or professional in the sciences or engineering, who has to solve a slew of Partial Differential Equations (PDEs). Often, the equations and boundary conditions mean that numerical analysis is required; analytic solutions are rare. The PDEs might be non-linear, which is another source of complexity and possible instability.

Finite element methods take up a large chunk of the text. The discussion is not restricted to the simple case where the space is divided into an equally spaced grid. He considers cases where you might need variable spacing; with a high concentration of grid points in regions of key interest. For example, think of solving for an electromagnetic field or fluid flow field, around a boundary of high curvature.

For linear systems, there is a foray into solving large matrix equations, where the matrices are sparse. Enough theory is developed to make the algorithms plausible.

Be aware that learning C++ thru this book won't give you all that C++ can do. Specifically, the string manipulations are little needed here. True of most computationally intensive code. But if you are not professionally a programmer, then this relative lack should not be a problem.
1 of 1 people found the following review helpful
5.0 out of 5 stars One of the best computational books and authors out there. 25 May 2011
By E Turner - Published on Amazon.com
Format:Hardcover|Verified Purchase
I highly recommend this author and his texts. The book combines theory, algorithm, pseudo-coding, and working code into an actual intelligible format which is very rare. If you are looking to create real working scientific code this is a must.
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