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Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities

Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities
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Year:    2009

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 4 : pp. 474–483

Abstract

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].

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/jcm.2009.27.4.014

Journal of Computational Mathematics, Vol. 27 (2009), Iss. 4 : pp. 474–483

Published online:    2009-01

AMS Subject Headings:   

Copyright:    COPYRIGHT: © Global Science Press

Pages:    10

Keywords:    Binomial coefficient Linear advection equations Immersed interface upwind scheme Piecewise constant coefficients Error estimates.

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