A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segme...A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.展开更多
In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation ...In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.展开更多
This article is concerned with the growth of energy of disturbances in a baroclinic flow within a finite time period. The implicit difference scheme was applied to the linearized vorticity equation, and the disturbanc...This article is concerned with the growth of energy of disturbances in a baroclinic flow within a finite time period. The implicit difference scheme was applied to the linearized vorticity equation, and the disturbance energy was computed for three kinds of vertical shears. It turns out that all the disturbance energy rapidly increases initially, and during the succeeding period there are several stages of growth and decay of energy of disturbances, and from a certain time on, all the disturbance energy begins to decrease.展开更多
基金Project supported by the National Natural Science Foundation of China(No.10671113)the Natural Science Foundation of Shandong Province of China(No.Y2003A04)
文摘A group of asymmetric difference schemes to approach the Korteweg-de Vries （KdV） equation is given here. According to such schemes, the full explicit difference scheme and the full implicit one, an alternating segment explicit-implicit difference scheme for solving the KdV equation is constructed. The scheme is linear unconditionally stable by the analysis of linearization procedure, and is used directly on the parallel computer. The numerical experiments show that the method has high accuracy.
基金The work was supported by Jiangsu Province's Natural Science Foundation (BK97004)National Natural Science Foundation (19801007) of CHINA.
文摘In this paper, the solution of back-Euler implicit difference scheme for a semi-linear parabolic equation is proved to converge to the solution of difference scheme for the corresponding semi-linear elliptic equation as t tends to infinity. The long asymptotic behavior of its discrete solution is obtained which is analogous to that of its continuous solution. At last, a few results are also presented for Crank-Nicolson scheme.
基金the National Natural Science Foundation of China (Grant No. 40775023)the ScientificResearch Special Item of Commonweal (Meteorology) KeyApplication Technology Study on Ensemble Forecast usingTIGGE Data (Grant No. GYHY (QX)2007-6-1)
文摘This article is concerned with the growth of energy of disturbances in a baroclinic flow within a finite time period. The implicit difference scheme was applied to the linearized vorticity equation, and the disturbance energy was computed for three kinds of vertical shears. It turns out that all the disturbance energy rapidly increases initially, and during the succeeding period there are several stages of growth and decay of energy of disturbances, and from a certain time on, all the disturbance energy begins to decrease.
