Stability and convergence of staggered Runge-Kutta schemes for semilinear wave equations |
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Authors: | Daisuke Murai Toshiyuki Koto |
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Institution: | a Graduate School of Information Science, Nagoya University, Furo-cho, Chikusa-ku, Nagoya 464-8601, Japanb Department of Information Systems and Mathematical Sciences, Nanzan University, 27 Seirei-cho, Seto, Aich 489-0863, Japan |
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Abstract: | A staggered Runge-Kutta (staggered RK) scheme is a Runge-Kutta type scheme using a time staggered grid, as proposed by Ghrist et al. in 2000 6]. Afterwards, Verwer in two papers investigated the efficiency of a scheme proposed by Ghrist et al. 6] for linear wave equations. We study stability and convergence properties of this scheme for semilinear wave equations. In particular, we prove convergence of a fully discrete scheme obtained by applying the staggered RK scheme to the MOL approximation of the equation. |
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Keywords: | Wave equations Explicit time integration Staggered Runge-Kutta schemes Convergence Stability analysis |
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