Finite Difference and Spectral Methods

1. G. E. Forsythe and W. R. Wasow, Finite-Difference Methods for Partial Differential Equations, Wiley, 1960.
2. D. Gottlieb and S. A. Orszag, Numerical Analysis of Spectral Methods: Theory and Applications, CBMS-NSF Regional Conference Series in Applied Mathematics, Vol. 26, SIAM, 1977.
3. B. Gustafsson, H.-O. Kreiss, and J. Oliger, Time Dependent Problems and Difference Methods, Wiley, 1995.
4. R. J. LeVeque, Numerical Methods for Conservation Laws, 2nd ed., Birkhäuser Verlag, 1992.
5. K. W. Morton and D. F. Mayers, Numerical Solution of Partial Differential Equations, Cambridge University Press, 1995.
6. R. D. Richtmyer and K. W. Morton, Difference Methods for Initial-value Problems, 2nd ed., Interscience, Wiley, 1967.
7. G. D. Smith, Numerical Solution of Partial Differential Equations: Finite Difference Methods, 3rd ed., Oxford University Press, 1986.
8. J. C. Strikwerda, Finite Difference Schemes and Partial Differential Equations, Chapman & Hall, 1989.
9. L. N. Trefethen, Spectral Methods in Matlab, SIAM, 2002.

Partial Differential Equations

1. W. A. Strauss, Partial differential Equations, An Introduction, Wiley, 1992.
2. M. Renardy and R.C. Rogers, An Introduction to Partial Differential Equations, Texts in Applied Mathematics 13, Springer-Verlag, 1992.
3. F. John, Partial differential Equations, Applied Mathematical Sciences 1, 4th ed., Springer-Verlag, 1982.
4. L. C. Evans, Partial differential Equations, Graduate Studies in Mathematics, Vol. 19, Amer. Math. Soc., 1998.
5. J. Smoller, Shock Waves and Reaction-Diffusion Equations, Springer-Verlag, 1983.