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

Hans Petter Langtangen
4.5 out of 5 stars  See all reviews (2 customer reviews)


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Computational Partial Differential Equations Computational Partial Differential Equations 4.5 out of 5 stars (2)
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Book Description

July 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.


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Review

The book explains the difficulties of the mathematics as well as the intricacies involved when the PDEs are ``linearized'' into systems of algebraic equations and solved in various ways. ... With each level of complexity, relevant sample problems are solved using the Diffpack software to demonstrate how the problem can be solved. My usual complaint for technical books is that they either go too far with examples and don't provide enough background, or they do the opposite and go too far with theory and leave the reader with no concrete way to apply it. In my opinion, this book has struck the balance well. I wholeheartedly recommend it as a general text on the topic. Summary: Excellent book, powerful software, well-written, well-documented, but steep learning curve. (The Linux Journal, December, 1999 (by Jim Moore)) -- The Linux Journal, December, 1999 (by Jim Moore)

Product Details

  • Series: Lecture Notes in Computational Science and Engineering (Book 2)
  • Hardcover: 682 pages
  • Publisher: Springer-Verlag Telos (July 1999)
  • Language: English
  • ISBN-10: 3540652744
  • ISBN-13: 978-3540652748
  • Product Dimensions: 9.6 x 6.4 x 1.2 inches
  • Shipping Weight: 2.5 pounds
  • Average Customer Review: 4.5 out of 5 stars  See all reviews (2 customer reviews)
  • Amazon Best Sellers Rank: #5,798,069 in Books (See Top 100 in Books)

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5 of 5 people found the following review helpful
4.0 out of 5 stars learn C++ via the book's examples July 6, 2008
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.
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1 of 1 people found the following review helpful
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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