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.
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Book Description
Editorial Reviews
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'... 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.
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21 of 30 people found the following review helpful:
4.0 out of 5 stars
Good Starter,
By Sathya. Kaliyamoorthy (Cleveland Heights, Ohio USA) - See all my reviews
This review is from: Numerical Solution of Partial Differential Equations (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.
3.0 out of 5 stars
Newer is not necessarily better.,
This review is from: Numerical Solution of Partial Differential Equations: An Introduction (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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Inside This Book
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First Sentence:
In this chapter we shall be concerned with the numerical solution of parabolic equations in one space variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
uniform square mesh, refinement path, new time level, previous time level, box scheme, derivative boundary conditions, upwind scheme, mesh function, iteration matrix, truncation error, linear advection, second order elliptic equations, mesh points, parabolic problems, maximum norm, explicit scheme, parabolic equations, maximum principle, hyperbolic equations, uniform mesh, difference scheme Key Phrases - Capitalized Phrases (CAPs): (learn more)
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In this chapter we shall be concerned with the numerical solution of parabolic equations in one space variable. Read the first page Key Phrases - Statistically Improbable Phrases (SIPs): (learn more)
uniform square mesh, refinement path, new time level, previous time level, box scheme, derivative boundary conditions, upwind scheme, mesh function, iteration matrix, truncation error, linear advection, second order elliptic equations, mesh points, parabolic problems, maximum norm, explicit scheme, parabolic equations, maximum principle, hyperbolic equations, uniform mesh, difference scheme Key Phrases - Capitalized Phrases (CAPs): (learn more)
Lax Equivalence Theorem New!
Books on Related Topics | Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
See all 11 books this book cites
67
books
cite this book:
See all 67 books citing this book
- Methods of Mathematical Physics, Vol. 1 by Richard Courant in Back Matter
- Direct Methods for Sparse Matrices (Monographs on Numerical Analysis) by I. S. Duff in Back Matter
- An Analysis of the Finite Element Method by William Gilbert Strang in Back Matter
- The Mathematics of Diffusion by John Crank in Back Matter
- Partial Differential Equations (Applied Mathematical Sciences) (v. 1) by Fritz John in Back Matter
See all 11 books this book cites
- Nonstandard Finite Difference Models of by Ronald E. Mickens on page 190, page 215, and Back Matter
- Computational Heat Transfer (Series in Computational and Physical Processes in Mechanics and Thermal Sciences) by Yogesh Jaluria on page 34, and page 82
- Modelling Financial Derivatives with MATHEMATICA ® by William T. Shaw on page 265, and page 305
- Numerical Simulations and Case Studies Using Visual C++.Net by Shaharuddin Salleh on page 49, and page 115
- Numerical Methods In Engineering and Science by Carl .E. Pearson on page 183
See all 67 books citing this book
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