THE l~1-STABILITY OF A HAMILTONIAN-PRESERVING SCHEME FOR THE LIOUVILLE EQUATION WITH DISCONTINUOUS POTENTIALS |
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| Authors: | Xin Wen LSEC ICMSEC Academy of Mathematics Systems Science Chinese Academy of Sciences Beijing China Shi Jin |
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| Institution: | Xin Wen LSEC,ICMSEC,Academy of Mathematics , Systems Science,Chinese Academy of Sciences,Beijing 100190,China Shi Jin Department of Mathematics,University of Wisconsin,Madison,WI 53706,USA |
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| Abstract: | We study the l~1-stability of a Hamiltonian-preserving scheme,developed in Jin and Wen,Comm.Math.Sci.,3 (2005),285-315],for the Liouville equation with a discontinuous potential in one space dimension.We prove that,for suitable initial data,the scheme is stable in the l~1-norm under a hyperbolic CFL condition which is in consistent with the l~1-convergence results established in Wen and Jin,SIAM J.Numer.Anal.,46 (2008), 2688-2714] for the same scheme.The stability constant is shown to be independent of th... |
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| Keywords: | Liouville equations Hamiltonian preserving schemes Discontinuous potentials l~1-stability Semiclassical limit |
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