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.
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About the Author
G. D. Smith is at Brunel University.
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13 of 14 people found the following review helpful:
5.0 out of 5 stars
Excellent introductory book on Finite Difference Method,
By A Customer
This review is from: Numerical Solution of Partial Differential Equations: Finite Difference Methods (Oxford Applied Mathematics & Computing Science Series) (Paperback)
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.
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