Abstract
In this chapter we deal with time-dependent problems of hyperbolic type. For their origin and an in-depth analysis see e.g. [Sal08, Chap. 4]. We will limit ourselves to considering the numerical approximation using the finite difference method, which was historically the first one to be applied to this type of equations. To introduce in a simple way the basic concepts of the theory, most of our presentation will concern problems depending on a single space variable. Finite element approximations will be addressed in Chapter 15, the extension to nonlinear problems in Chapter 16.
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Quarteroni, A. (2017). Finite differences for hyperbolic equations. In: Numerical Models for Differential Problems. MS&A, vol 16. Springer, Cham. https://doi.org/10.1007/978-3-319-49316-9_14
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DOI: https://doi.org/10.1007/978-3-319-49316-9_14
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Publisher Name: Springer, Cham
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Online ISBN: 978-3-319-49316-9
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