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.
CITATION STYLE
Quarteroni, A. (2017). Finite differences for hyperbolic equations. In Modeling, Simulation and Applications (Vol. 16, pp. 367–398). Springer-Verlag Italia s.r.l. https://doi.org/10.1007/978-3-319-49316-9_14
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