Stability for the finite difference solutions of the linear wave equation
2012
Hochschulschrift
Zugriff:
100
We consider in this paper methods of stability analysis for the finite difference solutions of the linear wave equation utt = uxx (0 < x < 1; t > 0). First, traditional methods, such as separation of variables, Von Neumann analysis are studied. Recently, Furihata [4] and Matuso [6] proposed the so-called discrete variational derivative method, which is applicable to our problem and gives several stable schemes, On the other hand, Samarskii et al. [11] considered difference equations defined in a finite-dimensional Hilbert space and analyzed the stability of their difference solutions. However all the methods mentioned above could not solve the stability for the most primitive explicit scheme (2) where nonuniform time meshes are taken into consideration. Thus we also introduce Cho's result [2], in which the stability is proved by a modified energy.
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Stability for the finite difference solutions of the linear wave equation
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Autor/in / Beteiligte Person: | Ciou, Bo-Siang ; 邱柏翔 |
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Veröffentlichung: | 2012 |
Medientyp: | Hochschulschrift |
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