CONVERGENCE OF AN IMMERSED INTERFACE UPWIND SCHEME FOR LINEAR ADVECTION EQUATIONS WITH PIECEWISE CONSTANT COEFFICIENTS Ⅱ: SOME RELATED BINOMIAL COEFFICIENT INEQUALITIES  

作　　者：Xin Wen 

机构地区：[1]LSEC, ICMSEC, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

出　　处：《Journal of Computational Mathematics》2009年第4期474-483,共10页计算数学（英文）

基　　金：supported in part by the Knowledge Innovation Project of the Chinese Academy of Sciences grants K5501312S1,K5502212F1,K7290312G7 and K7502712F7;NSFC grant 10601062

摘　　要：In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, （2008）, 1-22] to establish the L^1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L^1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, （2005）, 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, （2008）, 2688-2714].In this paper we give proof of three binomial coefficient inequalities. These inequalities are key ingredients in [Wen and Jin, J. Comput. Math. 26, （2008）, 1-22] to establish the L^1-error estimates for the upwind difference scheme to the linear advection equations with a piecewise constant wave speed and a general interface condition, which were further used to establish the L^1-error estimates for a Hamiltonian-preserving scheme developed in [Jin and Wen, Commun. Math. Sci. 3, （2005）, 285-315] to the Liouville equation with piecewise constant potentials [Wen and Jin, SIAM J. Numer. Anal. 46, （2008）, 2688-2714].

关 键 词：Binomial coefficient Linear advection equations Immersed interface upwindscheme Piecewise constant coefficients Error estimates. 

分 类 号：O241.84[理学—计算数学] TU311[理学—数学]