Finite-Difference Approximations for One-Dimensional Transport
As discussed in Chap. 1, one basic strategy for representing continuous functions on digital computers is through the set of values assumed by the function at a finite number of grid points. Such grid-point methods approximate derivatives of the original continuous function using finite differences. Finite differences were introduced in connection with the solution of ordinary differential equations in Sect. 2.1.1. In this chapter we examine the behavior of numerical schemes in which finite differences replace both time and space derivatives in time-dependent partial differential equations.
KeywordsTruncation Error Phase Speed Advection Equation Courant Number Compact Scheme
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