Book Description
This book provides a unified and accessible introduction to the basic theory of finite difference schemes applied to the numerical solution of partial differential equations. Originally published in 1989, its objective remains to clearly present the basic methods necessary to perform finite difference schemes and to understand the theory underlying these schemes. This is one of the few texts in the field to not only present the theory of stability in a rigorous and clear manner but also to discuss the theory of initial-boundary value problems in relation to finite difference schemes. In this updated edition the notion of a stability domain is now included in the definition of stability and is more prevalent throughout the book. The author has also added many new figures and tables to clarify important concepts and illustrate the properties of finite difference schemes.
Customer Reviews:
One of the best books ever.......2005-02-06
This book deals with the broad range of PDE problems with wonderful numerical algorithms.
I was crushed on the 1st edition because it was really well-balanced (i.e.,just necessary math but full coverage of real world interests) and well-organized book.
This book (the 2nd edition) includes more pictures and examples which help the reader to undersand the important concepts with ease.
Sometimes, the brief sentences seem to be too concise to the fist reader, but that is not true.
Once the reader understand the previous stuff, he or she does not need to look other books to understand the next stuff.
(Of cousre, this claim might not be applied to undergrads, because this book is inteneded to the first year grads. See preface.)
This book can be used as a text book in math or computer science class, but to engineers like me, this book is amzing even to the researchers who are closely got involved with physical modeling or simulation.
It is very difficult to meet good people, and it seems to be lucky if we meet those kinds of people.
This is also true for us to meet well-written books.
I feel I am very lucky to find this book.
Book Description
If you want top grades and thorough understanding of partial differential equations, this powerful study tool is the best tutor you can have! It takes you step-by-step through the subject and gives you 290 accompanying related problems with fully worked solutions. You also get plenty of practice problems to do on your own, working at your own speed. (Answers at the back show you how you're doing.) Famous for their clarity, wealth of illustrations and examples, and lack of dreary minutiae, SchaumÕs Outlines have sold more than 30 million copies worldwideÑand this guide will show you why!
Customer Reviews:
Partial Differential Equations review.......2007-01-04
I have found it helpful and inciteful with the more difficult differential equations that can be attempted.
Good if you've forgotten.......2006-04-22
This book contains mostly routine exercises of the subject. If you want to dig a bit further and sharpen your skills: try Krasnov's A Book of Problems in Ordinary Differential Equations. Language: English
ISBN: 5030009493
Not up to par with other Schaum's outlines on mathematics.......2006-04-21
This is one of the more poorly written Schaum's outlines I have encountered. The theory is very murky and the author gives no clear direction as to where he is going with this material and what it all means. PDE is a hard enough subject without working a bunch of meaningless problems that leave you wondering what it is you are supposed to have learned. Instead, I suggest you read "Introduction to Partial Differential Equations with Applications" by Zachmanoglou and Thoe in order to understand the mathematical underpinnings of PDE. Then read "Partial Differential Equations for Scientists and Engineers" to get a thorough feel for how PDE is used to solve real-world problems. Both books usually sell used for under $10 each, making them cost-effective alternatives to this Schaum's outline.
Duchateau a poor teacher.......2003-11-01
I have not read this book, but if it is anything like the author's previous attempts at writing it will leave you feeling angry. I read his advanced calculus book and it was awful. I found 16 mistakes on one page! This was the first book on advanced calculus I read and I was unable to follow the logic sequence. It wasn't until later after reading other books and mastering the subject that I discovered why. The examples were full of major errors. Not only that but he wastes a great deal of space repeating assumptions before each new section. As a result the actual material covered is sparse.
It is a very good book.......2003-06-15
This is a very good introduction to partial
differential equations.It contains the most
common methods in PDE namely: characteristics
method, Fourier method, Green method, finite
difference methods, variational methods and
finite element method. I have used it as a
textbook or suplementary text. It is really
an undergraduate text which provides a wide
introduction to PDE. I have a copy and recommend
it to every person interested in learning PDE.
Book Description
The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method.
In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature:
- Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options
- Early exercise features and approximation using front-fixing, penalty and variational methods
- Modelling stochastic volatility models using Splitting methods
- Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work
- Modelling jumps using Partial Integro Differential Equations (PIDE)
- Free and moving boundary value problems in QF
Included with the book is a CD containing information on how to set up FDM algorithms, how to map these algorithms to C++ as well as several working programs for one-factor and two-factor models. We also provide source code so that you can customize the applications to suit your own needs.
Download Description
The world of quantitative finance (QF) is one of the fastest growing areas of research and its practical applications to derivatives pricing problem. Since the discovery of the famous Black-Scholes equation in the 1970's we have seen a surge in the number of models for a wide range of products such as plain and exotic options, interest rate derivatives, real options and many others. Gone are the days when it was possible to price these derivatives analytically. For most problems we must resort to some kind of approximate method. In this book we employ partial differential equations (PDE) to describe a range of one-factor and multi-factor derivatives products such as plain European and American options, multi-asset options, Asian options, interest rate options and real options. PDE techniques allow us to create a framework for modeling complex and interesting derivatives products. Having defined the PDE problem we then approximate it using the Finite Difference Method (FDM). This method has been used for many application areas such as fluid dynamics, heat transfer, semiconductor simulation and astrophysics, to name just a few. In this book we apply the same techniques to pricing real-life derivative products. We use both traditional (or well-known) methods as well as a number of advanced schemes that are making their way into the QF literature: * Crank-Nicolson, exponentially fitted and higher-order schemes for one-factor and multi-factor options * Early exercise features and approximation using front-fixing, penalty and variational methods * Modelling stochastic volatility models using Splitting methods * Critique of ADI and Crank-Nicolson schemes; when they work and when they don't work * Modelling jumps using Partial Integro Differential Equations (PIDE) * Free and moving boundary value problems in QF
Customer Reviews:
A practical approach to finite difference methods.......2006-11-10
This book proved to be a useful reference for practical implementation of finite-difference methods for PDEs: several one- and multi-factor financial derivatives pricing models, including local volatility models and models with stochastic volatilities. The methods described in the text are stable, accurate and reasonably efficient. Stability of FD methods is obviously of top concern to the author (as it should be to readers as well), and he goes into extensive detail evaluating the stability of various techniques. The writing is clear and consistent, though a "notational" index or glossary would have been helpful, particularly in the early going. The author provides several practical examples, which lends a refreshing degree of concreteness to the book.
Well Done.......2006-11-06
Daniel J.Duffy introduces Finite Difference methods for solving partial differential equations that arise in numerical pricing of derivatives. There are seven sections in the book. They are:
Part I The Continuous Theory of Partial Differential Equations - A short introduction to partial differential equations and their applications to financial engineering.
Part II Finite Difference Methods: the Fundamentals - There are three chapters that introduce Finite Difference methods to approximate initial value and initial boundary value problems. Another two chapters apply the methods to Black-Scholes equation. He did a nice job to approximate the solutions to problems with small volatility or large drift,...
Part III Applying FDM to One-Factor Instrument Pricing
Part IV FDM for Multidimensional problems
Part V Applying FDM to Multi-Factor Instrument Pricing and
Part VI Free and Moving Boundary Value Problems
There are altogether 18 chapters (about 180 pages) that thoroughly introduce the application of FDM techniques to a wide range of options (pricing) modelling. The exposition is clear and concise.
The last part
Part VII Design and implementation In C++ - The last four chapters design for readers having programming literacy.
To fully appreciate the materials of the book, readers should have at least one year training in partial differential equations and knowledge in financial derivatives at about the same level as John Hull's book - Options, Futures and Other Derivatives, 5e.
If the book contains a few applications to real world data, it will be perfect to primers in this field.
Need more books like this one.......2006-07-05
Having bought many books in Financial Engineering this is one of the most useful. The source code is atleast alot better than the other books that claim to be the best. I give this book 4 stars and recommend quants to buy this book.
Book Description
This text will be divided into two books which cover the topic of numerical partial differential equations. Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student, this text offers a means of coming out of a course with a large number of methods which provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.
Customer Reviews:
Good, practical book for FDM applied to PDE.......2004-04-16
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.
(...)
Numerical Partial Differential Equations.......2000-01-20
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.
Book Description
Substantially revised, this authoritative study covers the standard finite difference methods of parabolic, hyperbolic, and elliptic equations, and includes the concomitant theoretical work on consistency, stability, and convergence. The new edition includes revised and greatly expanded
sections on stability based on the Lax-Richtmeyer definition, the application of Pade approximants to systems of ordinary differential equations for parabolic and hyperbolic equations, and a considerably improved presentation of iterative methods. A fast-paced introduction to numerical methods,
this will be a useful volume for students of mathematics and engineering, and for postgraduates and professionals who need a clear, concise grounding in this discipline.
Customer Reviews:
Excellent introductory book on Finite Difference Method.......2004-03-04
I first used this book a long time ago (1988) when the third edition of it just came out, while I just got a chance to write a review on it much much years after that. It was a required graduate textbook at an Ivy League college. It discussed in depth the finite difference technique applied to the parabolic, elliptic, and hyperbolic types of PDEs. The thing that I really like about this book is, besides having not too much details on mathematical derivations, it gives examples on how to do the calculations by hand. Thus when one would like to "translate" all these calculations into a computer program one could easily test the results (or expected results). Of course there are a lot more books out there talking about finite difference technique but they are perhaps 20 bucks or more expensive than this book. The only minus about this book is it was printed in soft cover, even though mine is still in a very good condition after almost 16 years! I recommend this book for those beginners on finite difference method. I am currently using this book for one of my course.
Average customer rating:
|
Applications of Nonstandard Finite Difference Schemes
Manufacturer: World Scientific Publishing Company
ProductGroup: Book
Binding: Hardcover
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Customer Reviews:
Potentially great.......2001-09-21
I have only had a borrowed copy for a few days, but this could be the biggest break through since the PC.
Everyone who models ODEs & PDEs with finite differences
should have this book.
Well written, but the math is dense.
Book Description
Of the many different approaches to solving partial differential equations numerically, this book studies difference methods. Written for the beginning graduate student in applied mathematics and engineering, this text offers a means of coming out of a course with a large number of methods that provide both theoretical knowledge and numerical experience. The reader will learn that numerical experimentation is a part of the subject of numerical solution of partial differential equations, and will be shown some uses and taught some techniques of numerical experimentation.
Prerequisites suggested for using this book in a course might include at least one semester of partial differential equations and some programming capability. The author stresses the use of technology throughout the text, allowing the student to utilize it as much as possible. The use of graphics for both illustration and analysis is emphasized, and algebraic manipulators are used when convenient. This is the second volume of a two-part book.
Average customer rating:
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Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
Victor G. Ganzha , and
E. V. Vorozhtsov
Manufacturer: Wiley-Interscience
ProductGroup: Book
Binding: Hardcover
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ASIN: 0471129461 |
Book Description
Advances in computer technology have conveniently coincided with trends in numerical analysis toward increased complexity of computational algorithms based on finite difference methods. It is no longer feasible to perform stability investigation of these methods manuallyâand no longer necessary. As this book shows, modern computer algebra tools can be combined with methods from numerical analysis to generate programs that will do the job automatically.
Comprehensive, timely, and accessibleâthis is the definitive reference on the application of computerized symbolic manipulations for analyzing the stability of a wide range of difference schemes. In particular, it deals with those schemes that are used to solve complex physical problems in areas such as gas dynamics, heat and mass transfer, catastrophe theory, elasticity, shallow water theory, and more.
Introducing many new applications, methods, and concepts, Computer-Aided Analysis of Difference Schemes for Partial Differential Equations
- Shows how computational algebra expedites the task of stability analysisâwhatever the approach to stability investigation
- Covers ten different approaches for each stability method
- Deals with the specific characteristics of each method and its application to problems commonly encountered by numerical modelers
- Describes all basic mathematical formulas that are necessary to implement each algorithm
- Provides each formula in several global algebraic symbolic languages, such as MAPLE, MATHEMATICA, and REDUCE
- Includes numerous illustrations and thought-provoking examples throughout the text
For mathematicians, physicists, and engineers, as well as for postgraduate students, and for anyone involved with numeric solutions for real-world physical problems, this book provides a valuable resource, a helpful guide, and a head start on developments for the twenty-first century.
Book Description
The book is suitable for advanced undergraduate and beginning graduate students of applied mathematics and engineering. The main theme is the integration of the theory of linear PDE and the theory of finite difference and finite element methods. For each type of PDE, elliptic, parabolic, and hyperbolic, the text contains one chapter on the mathematical theory of the differential equation, followed by one chapter on finite difference methods and one on finite element methods. The chapters on elliptic equations are preceded by a chapter on the two-point boundary value problem for ordinary differential equations. Similarly, the chapters on time-dependent problems are preceded by a chapter on the initial-value problem for ordinary differential equations. There is also one chapter on the elliptic eigenvalue problem and eigenfunction expansion. The presentation does not presume a deep knowledge of mathematical and functional analysis. The required background on linear functional analysis and Sobolev spaces is reviewed in an appendix.
Books:
- Finite Mathematics for Business Economics, Life Sciences and Social Sciences (10th Edition)
- Functional Analysis
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- Fundamentals of Physical Acoustics
- Galois Theory (Universitext)
- Geometry and the Imagination (CHEL/87.H) (AMS Chelsea Publishing)
- Handbook of Applied Cryptography (Crc Press Series on Discrete Mathematics and Its Applications)
- Handbook of Discrete and Combinatorial Mathematics
- Introduction to Algorithms
- Introduction to Management Science
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Partial Differential Equations: Methods and Applications (2nd Edition)
