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Volume 15, Issue 4
A New Class of Uniformly Second Order Accurate Difference Schemes for 2D Scalar Conservation Laws

Juan Cheng & Jiazun Dai

J. Comp. Math., 15 (1997), pp. 311-318.

Published online: 1997-08

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  • Abstract

In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws, we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the convergence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak $L^{\infty}$-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.

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@Article{JCM-15-311, author = {Cheng , Juan and Dai , Jiazun}, title = {A New Class of Uniformly Second Order Accurate Difference Schemes for 2D Scalar Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {1997}, volume = {15}, number = {4}, pages = {311--318}, abstract = {

In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws, we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the convergence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak $L^{\infty}$-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9208.html} }
TY - JOUR T1 - A New Class of Uniformly Second Order Accurate Difference Schemes for 2D Scalar Conservation Laws AU - Cheng , Juan AU - Dai , Jiazun JO - Journal of Computational Mathematics VL - 4 SP - 311 EP - 318 PY - 1997 DA - 1997/08 SN - 15 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9208.html KW - AB -

In this paper, concerned with the Cauchy problem for 2D nonlinear hyperbolic conservation laws, we construct a class of uniformly second order accurate finite difference schemes, which are based on the E-schemes. By applying the convergence theorem of Coquel-Le Floch [1], the family of approximate solutions defined by the scheme is proven to converge to the unique entropy weak $L^{\infty}$-solution. Furthermore, some numerical experiments on the Cauchy problem for the advection equation and the Riemann problem for the 2D Burgers equation are given and the relatively satisfied result is obtained.

Juan Cheng & Jiazun Dai. (1970). A New Class of Uniformly Second Order Accurate Difference Schemes for 2D Scalar Conservation Laws. Journal of Computational Mathematics. 15 (4). 311-318. doi:
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