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Accuracy of Lax-Wendroff scheme for discontinuous solutions of convection equations
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作者 DING LijuanDepartment of Applied Mathematics, Beijing Institute of Technology, Beijing 100081, China 《Chinese Science Bulletin》 SCIE EI CAS 1997年第24期2047-2051,共5页
IT is known from Brenner, Thomee and Wahlbin that the well-known second-order Lax-Wendroff scheme is stable in L^2, but unstable in L^p, p≠2. Generally speaking, if the initialdata is smooth enough and if a differenc... IT is known from Brenner, Thomee and Wahlbin that the well-known second-order Lax-Wendroff scheme is stable in L^2, but unstable in L^p, p≠2. Generally speaking, if the initialdata is smooth enough and if a difference scheme, which is stable in L^p for some p, has orderof accuracy μ, then we can expect that the solution of the difference scheme converges to thesolution of the differential equation at the rate of order μ in L^p. But for discontinuous solu-tions, which are essential to hyperbolic equations, the above expectation is not true. Error es-timates for discontinuous solutions not only have theoretical meaning, but also practical value. 展开更多
关键词 Lax-Wendroff scheme modlfled EQUATION DISCONTINUOUS solutions ERROR estimate.
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