In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(...In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.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
In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local trunc...In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.展开更多
In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as t -&g...In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as t -> infinity. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.展开更多
The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition ar...The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes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
In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in t...In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in time.The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived.Finally,some numerical tests are shown to verify our theoretical analysis.展开更多
文摘In this paper,a implicit difference scheme is proposed for solving the equation of one_dimension parabolic type by undetermined paameters.The stability condition is r=αΔt/Δx 2 1/2 and the truncation error is o(Δt 4+Δx 4) It can be easily solved by double sweeping method.
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.
文摘In this paper, an explicit three_level symmetrical differencing scheme with parameters for solving parabolic partial differential equation of three_dimension will be considered. The stability condition and local truncation error for the scheme are r<1/2 and O( Δ t 2+ Δ x 4+ Δ y 4+ Δ z 4) ,respectively.
文摘In this paper we prove that the solution of implicit difference scheme for a semilinear parabolic equation converges to the solution of difference scheme for the corresponding nonlinear stationary problem as t -> infinity. For the discrete solution of nonlinear parabolic problem, we get its long time asymptotic behavior which is similar to that of the continuous solution. For simplicity, we consider one-dimensional problem.
基金supported by the National Natural Science Foundation of China (No. 10971175)the Scientific Research Fund of Hunan Provincial Education Department (No. 09A093)
文摘The high-order implicit finite difference schemes for solving the fractional- order Stokes＇ first problem for a heated generalized second grade fluid with the Dirichlet boundary condition and the initial condition are given. The stability, solvability, and convergence of the numerical scheme are discussed via the Fourier analysis and the matrix analysis methods. An improved implicit scheme is also obtained. Finally, two numerical examples are given to demonstrate the effectiveness of the mentioned schemes
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.
基金the National Natural Science Fund(11661058,11301258,11361035)the Natural Science Fund of Inner Mongolia Autonomous Region(2016MS0102,2015MS0101)+1 种基金the Scientific Research Projection of Higher Schools of Inner Mongolia(NJZZ12011)the National Undergraduate Innovative Training Project(201510126026).
文摘In this paper,a nonlinear time-fractional coupled diffusion system is solved by using a mixed finite element(MFE)method in space combined with L1-approximation and implicit second-order backward difference scheme in time.The stability for nonlinear fully discrete finite element scheme is analyzed and a priori error estimates are derived.Finally,some numerical tests are shown to verify our theoretical analysis.
