This book presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject. In detail, topics covered include numerical solution of ordinary differential equations by multistep and Runge-Kutta methods; finite difference and finite elements techniques for the Poisson equation; a variety of algorithms to solve large, sparse algebraic systems; and methods for parabolic and hyperbolic differential equations and techniques of their analysis. The book is accompanied by an appendix that presents brief back-up in a number of mathematical topics.
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Editorial Reviews
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"As a mathematician who developed an interest in numerical analysis in the middle of his professional career, I thoroughly enjoyed reading this text. I wish this book had been available when I first began to take a serious interest in computation. The author's style is comfortable...This book would be my choice for a text to 'modernize' such courses and bring them closer to the current practice of applied mathematics." John Guckenheimer, American Journal of Physics
"...this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations and would serve perfectly as a textbook for a fourth-year undergraduate course in the mathematics curriculum." J. Varah, Computing Reviews
"The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject." Mathematical Reviews
"I bel;ieve this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations..." J. Varah, Computing Reviews
"...this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations and would serve perfectly as a textbook for a fourth-year undergraduate course in the mathematics curriculum." J. Varah, Computing Reviews
"The overall structure and the clarity of the exposition make this book an excellent introductory textbook for mathematics students. It seems also useful for engineers and scientists who have a practical knowledge of numerical methods and wish to acquire a better understanding of the subject." Mathematical Reviews
"I bel;ieve this book succeeds. It provides an excellent introduction to the numerical analysis of differential equations..." J. Varah, Computing Reviews
Book Description
This text presents a rigorous account of the fundamentals of numerical analysis of both ordinary and partial differential equations. The point of departure is mathematical but the exposition strives to maintain a balance among theoretical, algorithmic and applied aspects of the subject.
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Most Helpful Customer Reviews
8 of 8 people found the following review helpful:
4.0 out of 5 stars
Payback in longrun; not a Cookbook.,
By
This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)
In the graduate school, a Math professor used this book, as it talked about a bit of everything. Everything as in initial value problems (IVP) in ODE, 2 point boundary value problems ( BVP ) for ODE, finite difference schemes for boundary value elliptic PDE's and initial-boundary type hypebolic PDE's.However, the book is written for a mathematician in mind, as the author clearly mentions in the preface. It is not for the light hearted. Book would serve as a starting point for rigourous foundations in numerical analysis methods for solving ODE/PDE. Excellent book over all, with numerical examples, watertight arguments, and crisp prose, without being boring.
6 of 6 people found the following review helpful:
5.0 out of 5 stars
Excellent for a graduate course on numerical DE,
By Dennis Pence (Kalamazoo, MI USA) - See all my reviews
This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)
This is an excellent reference and textbook for someone hoping to go beyond the introduction to numerical DE found in any of the standard numerical analysis textbooks. It is not a research monograph, but is also not easy reading. It has already become a fairly standard reference in the literature because of its complete coverage and further references to more specialized sources. I have used it as the textbook for a graduate course on numerical differential equations. I highly recommend it for that purpose and as a reference for someone doing independent reading.
8 of 9 people found the following review helpful:
4.0 out of 5 stars
Informal, nice text,
This review is from: A First Course in the Numerical Analysis of Differential Equations (Cambridge Texts in Applied Mathematics) (Paperback)
A very informal style of writing with lots of explanation. He doesn't skip large steps like in the old-fashioned terse style of math texts, which makes it very readable, though some readers may not like it. Not very rigorous, but he's upfront about it.The original version from 1996 has quite a few errors, and the author maintains information on errata on his website. The most recent reprinting has corrected most of these errors. So, even though there is only a single edition, some versions have errors and some don't. So, BEWARE BUYING USED EDITIONS because they will most likely be from an earlier printing and thus have more errors. I assume the new version on amazon is the corrected version.
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Key Phrases - Statistically Improbable Phrases (SIPs):
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nonstiff problems, linear stability domain, spectral speed, classical iterative methods, second preconditioner, geometric numerical integration, complex unit disc, chapeau functions, monotone equations, theta method, line relaxation method, ordering vector, implicit midpoint rule, spectral convergence, computational stencil, stiff equations, advection equation, leapfrog method, nonlinear algebraic systems, isospectral flows, functional iteration, multistep methods, symplectic methods, waveform relaxation, error decays Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Fast Poisson, Acta Numerica, Cambridge University Press, Englewood Cliffs, Proof Let, Academic Press, Solving Ordinary Differential Equations, Proof According, Embedded Runge-Kutta, The Newton-Raphson, Springer Verlag, A-stability of Runge-Kutta, Numerical Initial Value Problems, Mathematics of Computation Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
nonstiff problems, linear stability domain, spectral speed, classical iterative methods, second preconditioner, geometric numerical integration, complex unit disc, chapeau functions, monotone equations, theta method, line relaxation method, ordering vector, implicit midpoint rule, spectral convergence, computational stencil, stiff equations, advection equation, leapfrog method, nonlinear algebraic systems, isospectral flows, functional iteration, multistep methods, symplectic methods, waveform relaxation, error decays Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Fast Poisson, Acta Numerica, Cambridge University Press, Englewood Cliffs, Proof Let, Academic Press, Solving Ordinary Differential Equations, Proof According, Embedded Runge-Kutta, The Newton-Raphson, Springer Verlag, A-stability of Runge-Kutta, Numerical Initial Value Problems, Mathematics of Computation Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Surprise Me!
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