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Volume 9, Issue 4
The Symmetrical Dissipative Difference Schemes for Quasi-Linear Hyperbolic Conservation Laws

Song-Bo Li

J. Comp. Math., 9 (1991), pp. 314-320.

Published online: 1991-09

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  • Abstract

In this paper we construct a new type of symmetrical dissipative difference scheme. Except discontinuity these schemes have uniformly second-order accuracy. For calculation using these, the simple-wave is very exact, the shock has high resolution, the programing is simple and the CPU time is economical.
Since the paper [1] introduced that in some conditions Lax-Wendroff scheme would converge to nonphysical solution, many researchers have discussed this problem. According to preserving the monotonicity of the solution preserving monotonial schemes and TVD schemes have been introduced by Harten, et. According to property of hyperbolic wave propagation the schemes of split-coefficient matrix (SCM) and split-flux have been formed. We emphasize the dissipative difference scheme, and these schemes are dissipative on arbitrary conditions.  

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@Article{JCM-9-314, author = {Li , Song-Bo}, title = {The Symmetrical Dissipative Difference Schemes for Quasi-Linear Hyperbolic Conservation Laws}, journal = {Journal of Computational Mathematics}, year = {1991}, volume = {9}, number = {4}, pages = {314--320}, abstract = {

In this paper we construct a new type of symmetrical dissipative difference scheme. Except discontinuity these schemes have uniformly second-order accuracy. For calculation using these, the simple-wave is very exact, the shock has high resolution, the programing is simple and the CPU time is economical.
Since the paper [1] introduced that in some conditions Lax-Wendroff scheme would converge to nonphysical solution, many researchers have discussed this problem. According to preserving the monotonicity of the solution preserving monotonial schemes and TVD schemes have been introduced by Harten, et. According to property of hyperbolic wave propagation the schemes of split-coefficient matrix (SCM) and split-flux have been formed. We emphasize the dissipative difference scheme, and these schemes are dissipative on arbitrary conditions.  

}, issn = {1991-7139}, doi = {https://doi.org/}, url = {http://global-sci.org/intro/article_detail/jcm/9406.html} }
TY - JOUR T1 - The Symmetrical Dissipative Difference Schemes for Quasi-Linear Hyperbolic Conservation Laws AU - Li , Song-Bo JO - Journal of Computational Mathematics VL - 4 SP - 314 EP - 320 PY - 1991 DA - 1991/09 SN - 9 DO - http://doi.org/ UR - https://global-sci.org/intro/article_detail/jcm/9406.html KW - AB -

In this paper we construct a new type of symmetrical dissipative difference scheme. Except discontinuity these schemes have uniformly second-order accuracy. For calculation using these, the simple-wave is very exact, the shock has high resolution, the programing is simple and the CPU time is economical.
Since the paper [1] introduced that in some conditions Lax-Wendroff scheme would converge to nonphysical solution, many researchers have discussed this problem. According to preserving the monotonicity of the solution preserving monotonial schemes and TVD schemes have been introduced by Harten, et. According to property of hyperbolic wave propagation the schemes of split-coefficient matrix (SCM) and split-flux have been formed. We emphasize the dissipative difference scheme, and these schemes are dissipative on arbitrary conditions.  

Li , Song-Bo. (1991). The Symmetrical Dissipative Difference Schemes for Quasi-Linear Hyperbolic Conservation Laws. Journal of Computational Mathematics. 9 (4). 314-320. doi:
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