O’Connor, William J. Wave speeds for a TLM model of moving media. (English) Zbl 0996.65090 Int. J. Numer. Model. 15, No. 2, 195-203 (2002). Summary: In a companion paper [ibid. 15, No. 2, 205-214 (2002; reviewed below)] a transmission line matrix (TLM) scheme is presented for the solution of the 1-D equation of waves in moving media, \(y_{tt}+ \alpha y_{xt}+ \beta y_{xx}= 0\), describing the superposition of two waves with direction-dependent speeds. The TLM model achieved controlled, direction-dependent wave-speed bias by means of supplementary link lines with notional ‘diodes’. Expressions for wave speed, presented without proof, were verified. Here a proof is presented using a new, time-domain approach. The apparent (direction-dependent) inductance and capacitance as seen by a single wave are first established in a generalized way from the TLM algorithm, from which two wave speeds and impedances are then derived. Cited in 1 Document MSC: 65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs 35L15 Initial value problems for second-order hyperbolic equations Keywords:transmission line matrix; moving media; wavespread; nonlinear waves; moving threadline Citations:Zbl 0996.65091 PDFBibTeX XMLCite \textit{W. J. O'Connor}, Int. J. Numer. Model. 15, No. 2, 195--203 (2002; Zbl 0996.65090) Full Text: DOI References: [1] O’Connor, International Journal of Numerical Modelling 15 pp 205– (2002) · Zbl 0996.65091 [2] Linear and Nonlinear Waves, Wiley: New York, 1974. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.