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In this chapter, we present a general analysis of partial differential equations (henceforth, PDEs). These are of importance here because the governing equations of the atmosphere and the ocean, including the hierarchy of simpler equations outlined in Chap. 1, belong to this class. We shall see that a PDE has a different character depending on the physics it describes. As we shall show in Chaps. 4– 6, this has to be taken into account when deciding which numerical method should be used to solve the PDE.
KeywordsPartial Differential Equations (PDE) Approximate Finite Difference (FDAs) Well-behaved Function Shallow Water Equations Quadrature Domains
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