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Volume 27, Issue 4
Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities

Xin Wen

DOI: 10.4208/jcm.2009.27.4.014

J. Comp. Math., 27 (2009), pp. 474-483.

Published online: 2009-08

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  • 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].

  • Keywords

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

  • AMS Subject Headings

05A20, 05A10, 65M15.

  • Copyright

COPYRIGHT: © Global Science Press

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@Article{JCM-27-474, author = {Xin Wen}, title = {Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities}, journal = {Journal of Computational Mathematics}, year = {2009}, volume = {27}, number = {4}, pages = {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].

}, issn = {1991-7139}, doi = {https://doi.org/10.4208/jcm.2009.27.4.014}, url = {http://global-sci.org/intro/article_detail/jcm/8584.html} }
TY - JOUR T1 - Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities AU - Xin Wen JO - Journal of Computational Mathematics VL - 4 SP - 474 EP - 483 PY - 2009 DA - 2009/08 SN - 27 DO - http://doi.org/10.4208/jcm.2009.27.4.014 UR - https://global-sci.org/intro/article_detail/jcm/8584.html KW - Binomial coefficient, Linear advection equations, Immersed interface upwind scheme, Piecewise constant coefficients, Error estimates. AB -

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].

Xin Wen. (2009). Convergence of an Immersed Interface Upwind Scheme for Linear Advection Equations with Piecewise Constant Coefficients II: Some Related Binomial Coefficients Inequalities. Journal of Computational Mathematics. 27 (4). 474-483. doi:10.4208/jcm.2009.27.4.014
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