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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.

Cheng , Juan and Dai , Jiazun. (1997). 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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