Phys. Rev. D 66, 104027 (2002) [11 pages]Discretizations of axisymmetric systemsReceived 25 July 2002; published 27 November 2002 In this paper we discuss stability properties of various discretizations for axisymmetric systems including the so-called cartoon method which was proposed by Alcubierre et al. for the simulation of such systems on Cartesian grids. We show that within the context of the method of lines such discretizations tend to be unstable unless one takes care in the way individual singular terms are treated. Examples are given for the linear axisymmetric wave equation in flat space. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevD.66.104027
DOI:
10.1103/PhysRevD.66.104027
PACS:
04.25.Dm
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