Abstract
In this chapter we simulate one-dimensional waves and analyze the numerical stability of simple integration algorithms. First we formulate the discretized wave equation as an eigenvalue problem and simulate waves on a finite string. We derive simple algorithms for direct integration of the discretized wave equation and discuss their stability properties. In a further computer experiment we study reflection at a closed or open boundary or at the border between two media with different refractive indices. We observe the effect of dispersion for pulses with different shape and duration.
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References
Solid-State Physics: An Introduction to Principles of Materials Science (Advanced Texts in Physics) Harald Ibach, Hans Lüth (Springer, Berlin, 2003)
R. Courant, K. Friedrichs, H. Lewy, Math. Annalen 100, 32 (1928)
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© 2010 Springer-Verlag Berlin Heidelberg
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Scherer, P.O. (2010). Waves. In: Computational Physics. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-13990-1_16
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DOI: https://doi.org/10.1007/978-3-642-13990-1_16
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Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-13989-5
Online ISBN: 978-3-642-13990-1
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