5 References

Some recommended books:

1. Claudio Canuto, M. Yousuff Hussaini, A. Quarteroni, & T. A. Zang Spectral Methods in Fluid Mechanics Springer-Verlag (1987) ISBN 3-540-17371-4 (Berlin) 0-387-17371-4 (New York). (Standard reference on spectral methods.)
2. Germund Dahlquist and Åke Björck Numerical Methods Prentice Hall (1974) ISBN 0-13-627315-7. (Excellent introduction to basic numerical methods.)
3. Paul DuChateau and David W Zachmann Partial Differential Equations Schaum's Outline Series, McGraw-Hill (1986) ISBN 0-07-017897-6.
4. Joel H. Ferziger Numerical Methods for Engineering Application Wiley (1981) ISBN 0-471-06336-3. (Stanford text.)
5. C.A.J. Fletcher Computational Techniques for Fluid Dynamics Vols. 1 and 2, Springer-Verlag (1988) ISBN 3-540-19466-5 (Berlin) 0-387-19466-5 (New York). (Good introduction to basic CFD.)
6. Bertil Gustafsson, Heinz-Otto Kreiss, and Joseph Oliger Time Dependent Problems and Difference Methods Wiley (1995) ISBN 0-471-50734-2. (Solid introduction to the fundamentals of finite difference methods.)
7. Wolfgang Hackbusch, Multi-Grid Methods and Application Springer-Verlag (1985) ISBN 0-387-12761-5.
8. Heinz Otto Kreiss Numerical Methods for Solving Time-Dependent problems for Partial Differential Equations Montreal: Les Presses de l'Universite de Montreal. Series: Seminaire de mathematiques superieures 65 (1978) ISBN 0840504306. (Read after Richtmyer & Morton.)
9. Leon Lapidus and George F. Pinder Numerical Solution of Partial Differential Equations in Science and Engineering Wiley-Interscience (1982) ISBN 0-471-09866-3. (Extensive reference on basic fundamentals.)
10. J.N. Reddy Functional Analysis and Variational Methods in Engineering McGraw-Hill (1986) ISBN 0-07-051348-1. (Read after Strang & Fix.)
11. Robert D. Richtmyer & K. W. Morton Difference Methods for Initial Value Problems Interscience, (1967) 2nd Ed. ISBN 0-470-72040-9. (Excellent but abstract introduction to the fundamentals of finite difference procedures.)
12. Gilbert Strang and George J. Fix An Analysis of the Finite Element Method Prentice-Hall, Englewood Cliffs, NJ (1973) ISBN 0-13-032946-0. (Excellent introduction to the fundamentals of the FE method.)
13. John C. Strikwerda Difference Schemes and Partial Differential Equations Wadsworth & Brooks/Cole, Belmont, CA (1989) ISBN 0-534-09984-X. (Solid introduction to the fundamentals of finite difference methods, but hard to read, many mistakes.)
14. Thomas A. Zang, C. L. Streett, & M. Y. Hussaini Spectral Methods for CFD ICASE Report No. 89-13, NASA CR 181803. (Similar to Canuto, but more concise, recent).