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Numerical Solution of Partial Differential Equations

3.3 out of 5 stars 3 customer reviews
ISBN-13: 978-0521429221
ISBN-10: 0521429226
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Editorial Reviews

Review

'... recommended to every student in applied mathematics and numerical analysis.' Numerical Algorithms

Book Description

Second edition of a highly succesful graduate text giving a complete introduction to partial differential equations and numerical analysis. Revised to include new sections on finite volume methods, modified equation analysis, multigrid, and conjugate gradient methods. The new text brings the reader up-to-date with the latest theoretical and industrial developments. --This text refers to the Digital edition.
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Product Details

  • Paperback: 239 pages
  • Publisher: Cambridge University Press (January 27, 1995)
  • Language: English
  • ISBN-10: 0521429226
  • ISBN-13: 978-0521429221
  • Product Dimensions: 6 x 0.7 x 9 inches
  • Shipping Weight: 13.1 ounces
  • Average Customer Review: 3.3 out of 5 stars  See all reviews (3 customer reviews)
  • Amazon Best Sellers Rank: #2,678,723 in Books (See Top 100 in Books)

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By David Schweitzer on October 24, 2015
Format: Paperback
This book is less concerned with actually solving numerical PDEs and discussing the methodologies behind how we develop the methods we use to approach them (which, for an ever growing field, is an absolute necessity) than it is in tackling the analytical background behind boundedness, iteration schemes, geometry, and basically the problem itself.

To be simpler, the idea in this book is more "These are the conditions in which we can develop a numerical scheme, and this is a good numerical scheme to use given the conditions" than it is "This is how we develop a numerical scheme."

Which is a useful topic, but unfortunately if one tried to apply this to, say, a typical program or course in Computational Fluid Dynamics, well, this book can be completely skipped and one can come out of said program or course knowing more about contributing to research in numerical methods (in general, not just with applications to fluid dynamics) than this book could ever provide.

HOWEVER.

For the person who is fully aware of the nature of some problem and wishes to find some numerical scheme to come up with, say, a quick presentation of efficiency in how said problem's solution accurately reflects a given model or physical data, then this book is pretty good for that, but I'm convinced you can find a better book elsewhere. It just seems too narrow a focus. For that, I agree with the other reviewer who described topics as "ad hoc."

On the other hand, this book is pretty demanding. Presentation is not entirely clear and a strong knowledge of PDEs and analysis (more aligned with mathematical analysis than a typical student's first few semesters in numerical analysis) are largely assumed.
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Format: Paperback
This book could be viewed as an abridged/updated version of the classic earlier text by the author. However, it has significantly less content than the earlier book. I'm not sure what to make of this book. No overall consistent theme. Some topics treated in an ad-hoc manner. The book is ok if you already know the material, but I can see that it would be difficult and confusing for a beginner in this field.

It appears to me that this book was written in order to remove all of the rigorous mathematical details of the Richtmyer and Morton book on Finite Difference Methods. I would not use this as a text for any course in numerical PDE. As strange as this may sound, books on CFD tend to do a better job at numerical analysis but a poor job at CFD! I would shop around until you find something you feel comfortable with. This one just doesn't do it for me.
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Format: Paperback
This book is a good starter for understanding how to numerically solve (Partial Differential Equations)PDE's. The chapters are arranged in an orderly manner and hints are provided then and there so that you wont need to switch back and forth between them. I myself a researcher in the field of Finite Element Analysis, which extensively involves PDE's for implementing the Finite element model. A thorough knowlegde of PDE's and the nature of their solutions is very important for such fields. This book is definitely the one which describes the nature of PDE's solutions and their interpretation, boundedness and applicability.
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