Stability and convergence of staggered Runge–Kutta schemes for semilinear wave equations

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摘要

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.

论文关键词:Wave equations,Explicit time integration,Staggered Runge–Kutta schemes,Convergence,Stability analysis

论文评审过程:Received 20 May 2010, Revised 5 February 2011, Available online 25 March 2011.

论文官网地址:https://doi.org/10.1016/j.cam.2011.03.020

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