Basic Finite-Difference Methods
As discussed in the preceding chapter, there are two conceptually different ways to represent continuous functions on digital computers: as a finite set of gridpoint values or as a finite set of series-expansion functions. The grid-point approach is used in conjunction with finite-difference methods, which were widely implemented on digital computers somewhat earlier than the series-expansion techniques. In addition, the theory for these methods is somewhat simpler than that for series-expansion methods. We will parallel this historical development by studying finite-difference methods in this chapter and deferring the treatment of series expansion methods to Chapter 4. Moreover, it is useful to understand finitedifference methods before investigating series-expansion techniques because even when series expansions are used to represent the spatial dependence of some atmospheric quantity, the time dependence is almost always discretized and treated with finite differences.
KeywordsTruncation Error Phase Speed Amplification Factor Advection Equation Courant Number
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