Reading List for MATH3474, MATH3475 & MATH5476M
New for 2011-12: Check out
the online books below, and search for
others.
Numerical methods for ODEs and PDEs is a
rapidly expanding field, with cutting-edge research continuing to develop in
this vast area. Accordingly, the following book list could never be complete,
so if there are any books which you feel should be included, or which are not
in the Leeds University Library, please email
me and I shall endeavour to order a copy, or check here
to see if the book is still in print.
Where an author's name is highlighted
below, the link will show you the location
and loan
status of the book in the Library, whose
Catalogue-Search page is here.
Over the years, I have found many of the
following books to be extremely useful. Some are aimed at a research level,
others are more suited towards teaching. Among them are some excellent and
well-known texts in each of the sub-areas considered in the course: these are
either recommended (*)
or highly
recommended (**)for the course; the book marked (***) is superb, albeit at research-level The other texts will almost certainly be of
interest/use to postgraduate students attending the course.
The omission of current book prices, which
have a habit of changing rapidly and/or being depressingly high, is deliberate.
- Finite-Difference Methods
- **G
D Smith, Numerical solution of partial differential equations:
finite-difference methods (3rd edn.), Oxford University Press, 1985 (ISBN
0 198 59650 2).
- * C
Hirsch, Numerical computation of internal and external flows: volume
1 - fundamentals of numerical discretization, Wiley, 1988 (ISBN 0 471
91762 1). Postgraduate-level
finite differences.
- Numerical Analysis
- ** K
E Atkinson, Elementary numerical analysis (2nd edn.), Wiley, 1993
(ISBN 047150999X). Excellent ; entry-level.
- ** K
E Atkinson, An introduction to numerical analysis (2nd edn.), Wiley,
1989 (ISBN 0471624896). Excellent
; more advanced.
- * R
L Burden & J D Faires, Numerical analysis (8h edn.), Brooks/Cole,
2005 (ISBN 0534404995). Recommended
text for MATH2600.
- S
D Conte & C de Boor, Elementary numerical analysis: an algorithmic
approach (3rd edn.), McGraw-Hill, 1980 (ISBN 0070124477).
- ** J
C Mason & D C Handscomb, Chebyshev polynomials, Chapman and Hall,
CRC, 2003 (ISBN 0 849 303 559). Excellent; online version here.
- M
J D Powell, Approximation theory and methods, Cambridge University
Press, 1981 (ISBN 0521295149)). A classic.
- ** A
Ralston & P Rabinowitz, A first course in numerical analysis (2nd
edn.),
- *H
R Schwarz, Numerical analysis : a comprehensive introduction, Wiley,
1989 (ISBN 0471920657). Very
good; thorough; advanced; added to library Oct. 2007.
- Finite-Element Methods
- R
D Cook, D S Malkus, M E Plesha & R J Witt, Concepts and
applications of finite-element analysis (4th ed.), Wiley, 2002 (ISBN 0
471 35605 0 ).
- * A
J Davies, The finite element method: a first approach, Oxford
University Press, 1980 (ISBN 0 198 59631 6).
- C Johnson,
Numerical solutions of partial differential equations by the
finite-element method, Cambridge University Press, 1987 (ISBN 0 521 34758
0).
- *J
Fish & T Belytschko, A first course in finite elements, Wiley,
2007 (ISBN 9 780 470 03580 1). Very clear book. Added to the library April 2008 .
- Boundary-Integral Methods
- W
Hackbusch, Integral equations: theory and numerical treatment,
Birkh„user Verlag, 1995 (ISBN 0 817 62871 1).
- M
A Jaswon & G T Symm, Integral equation methods in potential
theory and elastostatics, Academic Press, 1977 (ISBN 0 123 81050 7).
- R
Kress, Linear integral equations (2nd ed.), Springer Verlag, 1999
(ISBN 0 387 98700 2).
- *J
Trevelyan, Boundary elements for engineers: theory and applications,
Computational Mechanics Publications, 1994 (ISBN 1 853 12279 3).
- L
C Wrobel, The boundary element method (2 vols.), Wiley, 2001 (ISBN 0
471 72039 9 (Vol. 1) 0 470 84298 9 (Vol. 2)).
- Spectral Methods and FFTs
- *** J
P Boyd, Chebyshev and Fourier spectral methods (2nd edn.),
- C Canuto, Spectral methods in fluid dynamics, Springer Verlag, 1988
(ISBN 3 540 52205 0).
- * B
Fornberg, A practical guide to pseudospectral methods, Cambridge
University Press, 1998 (ISBN 0 521 64564 6).
- ** L
N Trefethen, Spectral methods in
- L
N Trefethen, Finite difference and spectral methods for ordinary and partial
differential equations, 1994. This is a never-completed free Web version.
- *J
S Walker, Fast Fourier transforms (2nd ed.), CRC Press, 1996 (ISBN 0
849 37163 5). Software disk available at Library counter.
- Multi-Grid Methods
- W
Hackbusch, Multi-grid methods and applications, Springer Verlag, 1985
(ISBN 0 387 12761 5). Reprinted in 2003.
- Partial Differential Equations
- K
E Gustafson, Introduction to partial differential equations and
Hilbert space methods (3rd edn.),
- **A
Iserles, A first course in the numerical analysis of differential
equations, Cambridge University Press, 1996 (ISBN 0 521 55655 4). Excellent;
a second
edition was published in 2008, adding new chapters on geometric
numerical integration, spectral methods and conjugate gradients.
- *W
E Williams, Partial differential equations, Oxford University Press,
1980 (ISBN 0 198 59633 2).
- E
Zauderer, Partial differential equations of applied mathematics (2nd
edn.), Wiley, 1989 (ISBN 0 471 31516 8).
- Computation, Linear Algebra and Maple
- O
Axelsson, Iterative solution methods, Cambridge University Press,
1996 (ISBN 0 521 55569 8).
- C
F Gerald & P O Wheatley, Applied numerical analysis (7th edn.),
Addison-Wesley, 2004 (ISBN 0 321 19019 x).
- ** F
G Garvan, The Maple Book, Chapman and Hall
(CRC), 2002 (ISBN 1 584 88232 8). Online version here.
- G
H Golub & C F van Loan, Matrix computations (3rd edn.), Johns
Hopkins University Press, 1996 (ISBN 0 801 85404 8).
- ** A
Heck, Introduction to Maple (3nd edn.),
Springer Verlag, 2003 (ISBN 0 387 00230 8). 3rd edition
extensively updated for Maple 9.
- N
J Higham, Accuracy and stability of numerical algorithms (2nd edn.),
- A
Jennings & J J McKeown, Matrix computation (2nd edn.), Wiley,
1992 (ISBN 0 471 93527 1).
