Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit θ-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The s...Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit θ-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when θ is closed to 1/2 even if we have variable coefficients.展开更多
This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incr...This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.展开更多
The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability ...The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.展开更多
Ranging from Re=100 to Re=20,000,several computational experiments are conducted,Re being the Reynolds number.The primary vortex stays put,and the longterm dynamic behavior of the small vortices determines the nature ...Ranging from Re=100 to Re=20,000,several computational experiments are conducted,Re being the Reynolds number.The primary vortex stays put,and the longterm dynamic behavior of the small vortices determines the nature of the solutions.For low Reynolds numbers,the solution is stationary;for moderate Reynolds numbers,it is time periodic.For high Reynolds numbers,the solution is neither stationary nor time periodic:the solution becomes chaotic.Of the small vortices,the merging and the splitting,the appearance and the disappearance,and,sometime,the dragging away from one corner to another and the impeding of the merging—these mark the route to chaos.For high Reynolds numbers,over weak fundamental frequencies appears a very low frequency dominating the spectra—this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been attained.The global attractor seems reached for Reynolds numbers up to Re=15,000.This is the lid-driven square cavity flow;the motivations for studying this flow are recalled in the Introduction.展开更多
基金This project is partially supported by Natural Science Foundation of Gansu Province under Grant 3ZS041-A25-011 by National Natural Science Foundation under Grant 10471056.
文摘Based on the finite difference discretization of partial differential equations, we propose a kind of semi-implicit θ-schemes of incremental unknowns type for the heat equation with time-dependent coefficients. The stability of the new schemes is carefully studied. Some new types of conditions give better stability when θ is closed to 1/2 even if we have variable coefficients.
文摘This paper deals with the special nonlinear reaction-diffusion equation. The finite difference scheme with incremental unknowns approximating to the differential equation （2.1） is set up by means of introducing incremental unknowns methods. Through the stability analyzing for the scheme, it was shown that the stability conditions of the finite difference schemes with the incremental unknowns are greatly improved when compared with the stability conditions of the corresponding classic difference scheme.
文摘The main purpose of this paper is to set up the finite difference scheme with incremental unknowns for the nonlinear differential equation by means of introducing incremental unknowns method and discuss the stability of the scheme.Through the stability analyzing for the scheme,it was shown that the stability of the finite difference scheme with the incremental unknowns is improved when compared with the stability of the corresponding classic difference scheme.
基金supported in part by the National Science Foundation Grant No.DMS-0604235.
文摘Ranging from Re=100 to Re=20,000,several computational experiments are conducted,Re being the Reynolds number.The primary vortex stays put,and the longterm dynamic behavior of the small vortices determines the nature of the solutions.For low Reynolds numbers,the solution is stationary;for moderate Reynolds numbers,it is time periodic.For high Reynolds numbers,the solution is neither stationary nor time periodic:the solution becomes chaotic.Of the small vortices,the merging and the splitting,the appearance and the disappearance,and,sometime,the dragging away from one corner to another and the impeding of the merging—these mark the route to chaos.For high Reynolds numbers,over weak fundamental frequencies appears a very low frequency dominating the spectra—this very low frequency being weaker than clear-cut fundamental frequencies seems an indication that the global attractor has been attained.The global attractor seems reached for Reynolds numbers up to Re=15,000.This is the lid-driven square cavity flow;the motivations for studying this flow are recalled in the Introduction.
