Abstract
In practice the algebraic equations that result from the discretisation process, Sect. 3.1, are obtained on a finite grid. It is to be expected, from the truncation errors given in Sects. 3.2 and 3.3, that more accurate solutions could be obtained on a refined grid. These aspects are considered further in Sect. 4.4. However for a given required solution accuracy it may be more economical to solve a higher-order finite difference scheme on a coarse grid than a low-order scheme on a finer grid, if the exact solution is sufficiently smooth. This leads to the concept of computational efficiency which is examined in Sect. 4.5.
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© 1998 Springer-Verlag Berlin Heidelberg
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Fletcher, C.A.J. (1998). Theoretical Background. In: Computational Techniques for Fluid Dynamics 1. Springer Series in Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-58229-5_4
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DOI: https://doi.org/10.1007/978-3-642-58229-5_4
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