Finite difference

Basics - covered on the Basic discretization techniques page... covered by Tannehill Chapter 3

Error analysis - Tannehill Chapter 3.6 (Fourier and von Neumann analysis)

Explicit, implicit, higher-order, nonlinear, etc. - Tannehill Chapter 4

References

Tannehill, John C.; Anderson, Dale A.; Pletcher, Richard H. (1997). Computational Fluid Mechanics and Heat Transfer (2nd ed.). Taylor and Francis.