Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics) [Hardcover]

J.W. Thomas (Author)

Book Description

ISBN-10: 0387979999 | ISBN-13: 978-0387979991 | Publication Date: September 11, 1995

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.

Editorial Reviews

Review

"This important volume is the first part of a two-part textbook (the second part is entitled Conservation laws and elliptic equations). The text includes interesting homework problems that implement different aspects of most of the schemes discussed. The implementation aspect of this text includes a large amount of computing. Other useful aspects of computing included in this volume are symbolic computing and the use of graphics for analysis. Prerequisites suggested for using this book might include one semester of partial differential equations and some programming capability. This book will be a good reference text for students." -- MATHEMATICAL REVIEWS

Product Details

• Hardcover: 480 pages
• Publisher: Springer (September 11, 1995)
• Language: English
• ISBN-10: 0387979999
• ISBN-13: 978-0387979991
• Product Dimensions: 9.4 x 6.4 x 1.3 inches
• Shipping Weight: 1.7 pounds (View shipping rates and policies)
• Average Customer Review: 4.0 out of 5 stars  See all reviews (2 customer reviews)
• Amazon Best Sellers Rank: #702,122 in Books (See Top 100 in Books)

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Customer Reviews

Most Helpful Customer Reviews

17 of 18 people found the following review helpful:

4.0 out of 5 stars Numerical Partial Differential Equations, January 19, 2000

By 

Alex Levin (New York) - See all my reviews

This review is from: Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics) (Hardcover)

Thomas wrote a good book on a quite specialized subject. Although finite difference schemes have been traditionally viewed as a game field for physicists, they are given today much more commercial attention as financial option market evolves. Those who seek standard numerical recipes are advised to read this book. You will enjoy it (easy reading) and learn. But the book may not satisfy quests of a more rigorous readership. It abuses the Fourier method in stability analysis while considering only PDEs with constant coefficients. The bibliographical work has not been done at all. In addition, the cover does not state that this is the first book of two. I'd also advise to read G.Marchuk "Methods of Numerical Mathematics" (Springer, 1982) where a more general approach for stability of numerical schemes is developed.

13 of 13 people found the following review helpful:

4.0 out of 5 stars Good, practical book for FDM applied to PDE, April 16, 2004

By 

Daniel Duffy (Amsterdam, The Netherlands) - See all my reviews

This review is from: Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics) (Hardcover)

This is a book that approximates the solution of parabolic, first order hyperbolic and systems of partial differential equations using standard finite difference schemes (FDM). The theory and practice of FDM is discussed in detail and numerous practical examples (heat equation, convection-diffusion) in one and two space variables are given. In particular, Alternating Direction Implicit (ADI) methods are the standard means of solving PDE in 2 and 3 dimensions.
In almost all cases model problems are taken in order to show how the schemes work for initial value problems, initial boundary value problem with Dirichlet and Neumann boundary conditions.
This book is a *must* for those in science, engineering and quantitative financial analysis. It digs into the nitty-gritty of mapping a PDE to a FDM scheme while taking nasty boundary conditions into consideration. The resulting algorithms are documented are are easily programmed in C++ or other language.
The book does not cover topics that are also important: operator splitting (Marchuk/Janenko), non-constant coefficient PDEs, nonlinearities. Finally, the book uses von Neumann analysis as a means of proving stability (getting a bit long in the tooth). There are more robust methods that use monotone schemes, M-matrices and the maximum principle. You should consult other specialised references.
This is Volume I of a two-volume set (Volume II deals with Conversation Laws and first-order hyperbolic as well as Elliptic problems.

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