Finite-Difference Approximations for One-Dimensional Transport

Part of the Texts in Applied Mathematics book series (TAM, volume 32)


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.


Truncation Error Phase Speed Advection Equation Courant Number Compact Scheme 


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Copyright information

© Springer Science+Business Media, LLC 2010

Authors and Affiliations

  1. 1.Department of Atmospheric SciencesUniversity of WashingtonSeattleUSA

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