Free Ebook Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics), by J.W. Thomas
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Numerical Partial Differential Equations: Finite Difference Methods (Texts in Applied Mathematics), by J.W. Thomas
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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.
- Sales Rank: #604622 in Books
- Published on: 2010-01-12
- Released on: 2010-01-12
- Original language: English
- Number of items: 1
- Dimensions: 9.25" h x 1.04" w x 6.10" l, 1.41 pounds
- Binding: Paperback
- 437 pages
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
Most helpful customer reviews
19 of 19 people found the following review helpful.
Good, practical book for FDM applied to PDE
By Daniel Duffy
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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18 of 19 people found the following review helpful.
Numerical Partial Differential Equations
By Alex Levin
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.
0 of 0 people found the following review helpful.
Good but has errors
By Officer_007
I had to read chapter 5 of this book for part of the comprehensive examination towards my PhD program. It is pretty easy to follow, except most of the steps in deriving equations are skipped. At times, this may be confusing for the reader. I went through the steps on my own to make sure I understood how one equation led to the other. For the most part, if one knows the fundamentals of numerical methods, it's just writing down the steps to come to the same conclusion.
What bothered me most was HW.5.6.8 (and 5.6.9). Basically, the problem is wrong. Such boundary conditions and initial conditions for the PDE given in the problem is not possible. I thought I was doing things wrong, so I took the problem to couple professors and other students and the conclusion was that the boundary condition that is given for that problem and the one after it can not be satisfied. Also, the given initial condition can only be thought of in imagination and not through analytical solution to the actual PDE. My three different numerical solutions match perfectly, but not the assumed anaylical solution f(x-at). So, I took one star off - also for a typo/mistake I found when stability of explicit FTCS method was discussed.
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