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Numerical Solution of Partial Differential Equations, by K. W. Morton, D. F. Mayers
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Partial differential equations are the chief means of providing mathematical models in science, engineering and other fields. Generally these models must be solved numerically. This book provides a concise introduction to standard numerical techniques, ones chosen on the basis of their general utility for practical problems. The authors emphasise finite difference methods for simple examples of parabolic, hyperbolic and elliptic equations; finite element, finite volume and spectral methods are discussed briefly to see how they relate to the main theme. Stability is treated clearly and rigorously using maximum principles, energy methods, and discrete Fourier analysis. Methods are described in detail for simple problems, accompanied by typical graphical results. A key feature is the thorough analysis of the properties of these methods. Plenty of examples and exercises of varying difficulty are supplied. The book is based on the extensive teaching experience of the authors, who are also well-known for their work on practical and theoretical aspects of numerical analysis. It will be an excellent choice for students and teachers in mathematics, engineering and computer science departments seeking a concise introduction to the subject.
- Sales Rank: #2940617 in Books
- Brand: Brand: Cambridge University Press
- Published on: 1995-01-27
- Original language: English
- Number of items: 1
- Dimensions: 8.98" h x .71" w x 5.98" l,
- Binding: Paperback
- 239 pages
- Used Book in Good Condition
Review
'... recommended to every student in applied mathematics and numerical analysis.' Numerical Algorithms
Most helpful customer reviews
0 of 0 people found the following review helpful.
Almost misleading in the title, but okay enough for what it presents.
By David Schweitzer
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.
In summary, this book is more about the nature of PDEs and the existence of numerical schemes than actually constructing schemes. Yes, construction is done, but it's so glossed over it seems more of a footnote. And the focus is too narrow to be readily accessible for someone looking for some ideas into numerical PDE methods.
If you're a student just taking a class, fine, whatever. But if you're someone who for some reason has stumbled into something that needs to be solved and you're looking for insights into how numerical analysts approach PDEs, go somewhere else.
2 of 2 people found the following review helpful.
Newer is not necessarily better.
By A. I. Haque
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.
21 of 30 people found the following review helpful.
Good Starter
By Sathya. Kaliyamoorthy
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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