Mathematics of Computation

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ISSN 1088-6842(e) ISSN 0025-5718(p)

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Book reviews do not contain an abstract. You may download the entire set of reviews from this issue using the links below.

Review information:

Journal: Math. Comp. 70, 1335-1352
DOI: 10.1090/S0025-5718-01-01388-6
PII: S 0025-5718(01)01388-6
Posted: March 30, 2001
Copyright of article: Copyright 2001, American Mathematical Society
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$p$ - and $hp$ -finite element methods. Theory and applications in solid and fluid mechanics, by Ch. Schwab
Oxford Science Publications, Clarendon Press, 1998, xii+374, $85.00
2000 Mathematics Subject Classification. Primary 65N30, 75V05, 76M10

Reviewed by: Mark Ainsworth
Affiliation: Mathematics Department, University of California Los Angeles, Los Angeles, CA 90095-1555

References:

[1]: B. Szabó and I. Babuska, Finite Element Analysis, John Wiley and Sons, Inc., 1991.
[2]: G. Em. Karniadakis and S. Sherwin, Spectral/hp Element Methods for CFD, Oxford University Press, 1999.

Spectral methods in Matlab, by Lloyd N. Trefethen
SIAM, Philadelphia, PA, 2000, xvi+165, $36.00
2000 Mathematics Subject Classification. Primary 41A10, 42A10, 65M70, 65T10

Reviewed by: Chi-Wang Shu

Generalized difference methods for differential equations. Numerical analysis of finite volume methods, by Ronghua Li, Zhongying Chen and Wei Wu
Marcel Dekker, New York, 2000, xv+442, $175.00
2000 Mathematics Subject Classification. Primary 65-02, 65N06, 65N30

Reviewed by: Raytcho Lazarov
Affiliation: Department of Mathematics, Texas A&M University, College Station, Texas 77843

References:

[1]: P. Ciarlet, The finite element method for elliptic problems, North-Holland, 1978.
[2]: B. Heinrich, Finite difference methods on irregular networks, ISNM 82, Birkhauser Verlag, 1987.
[3]: A. A. Samarskii, Introduction to the theory of finite difference schemes, Nauka, Moscow, 1972. (Russian)
[4]: A. A. Samarskii, R. D. Lazarov, and V. L. Makarov, Finite difference schemes for differential equations with generalized solutions, Visshaya Shkola, Moscow, 1987. (Russian)
[5]: R. Vilsmeier and F. Benkhaldoun, Editors, Finite Volumes for Complex Applications. I. Problems and Perspectives, Hermes Science Publications, Paris, 1997.
[6]: R. Vilsmeier, F. Benkhaldoun, and D. Hannel, Editors, Finite Volumes for Complex Applications. II. Problems and Perspectives, Hermes Science Publications, Paris, 1999.

Computer methods for ordinary differential equations and differential-algebraic equations, by Uri M. Ascher and Linda R. Petzold
SIAM, Philadelphia, PA, 1998, xvii+314, $36.50
2000 Mathematics Subject Classification. Primary 65-01, 65L05, 65L06, 65L10, 65L12, 65L99

Reviewed by: Rozwitha März
Affiliation: Institute of Mathematics, Humboldt-University of Berlin, D-10099 Berlin, Germany

References:

1.: Lawrence F. Shampine and Marilyn Gordon, Computer solution of ordinary differential equations. The initial value problem, W. H. Freemann and Company, San Francisco, 1975.
2.: Josef Stoer and Roland Bulirsch, Numerische Mathematik 2. Third edition, Springer-Verlag, 1990.
3.: Gene H. Golub and James M. Ortega, Scientific computing and differential equations. An introduction to numerical methods, Academic Press, Inc., 1981, 1992.

Geometric integration: numerical solution of differential equations, edited by C. J. Budd and A. Iserles
Philosophical Transactions of the Royal Society, Mathematical, Physical and Engineering Sciences, The Royal Society, UK, April 1999, vol. 157, no. 1754, pp. 943--1133
2000 Mathematics Subject Classification. Primary 65L05, 34A50, 58F99

Reviewed by: Ernst Hairer
Affiliation: Université de Geneve, Section de Mathematiques, 2 rue Du Lievre, CP240, CH-1211 Geneva 24, Switzerland

Dynamical systems and numerical analysis, by A. M. Stuart and A. R. Humphries
Cambridge University Press, New York, 1998, xxi+685, $65.95, softcover $39.95
2000 Mathematics Subject Classification. Primary 37Mxx, 65Pxx

Reviewed by: Rozwitha März
Affiliation: Institute of Mathematics, Humboldt-University of Berlin, D-10099 Berlin, Germany

Computer solution of large linear systems, by Gerard Meurant
North Holland, Amsterdam, 1999, xxii+753, $149.50
2000 Mathematics Subject Classification. Primary 65N30, 75V05, 76M10

Reviewed by: Brian Suchomel
Affiliation: Department of Computer Science and Engineering, University of Minnesota, Minneapolis, Minnesota 55455

Character sums with exponential functions and their applications, by Sergei Konyagin and Igor Shparlinski
Cambridge University Press, New York, 1999, viii+163, $49.95
2000 Mathematics Subject Classification. Primary 11L05, 11L40, 65C10, 94A60, 94B05

Reviewed by: Harald Niederreiter

The algorithmic resolution of Diophantine equations, by Nigel P. Smart
Cambridge University Press, New York, 1999, xvi+243, $69.95, softcover $26.95
2000 Mathematics Subject Classification. Primary 11-02, 11Dxx

Reviewed by: P. G. Walsh
Affiliation: Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, Ontario, Canada, K1N-6N5
E-mail address: gwalsh@mathstat.uottawa.ca


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