Constructions and Applied Examinations of a Kind of Square-Conservative Schemes in High Precision in the Time Direction

In order to meet the needs of work in numerical weather forecast and in numerical simulations for climate change and ocean current, a kind of difference scheme in high precision in the time direction developed from the completely square-conservative difference scheme in explicit way is built by means of the Taylor expansion. A numerical test with 4-wave Rossby-Haurwitz waves on them and an application of them on the monthly mean current the of South China Sea are carried out, from which, it is found that not only do the new schemes have high harmony and approximate precision but also can the time step of the schemes be lengthened and can much computational time be saved. Therefore, they are worth generalizing and applying.

Computational uncertainty and optimal grid size and time step of the Lax-Friedrichs scheme for the 1D advection equation

本文对于应用Lax-Friedrichs格式数值求解一维平流方程,研究数值求解过程中产生的截断误差与舍入误差,以及两种误差逐层向高时间层传播的累积,得到新的数值解总误差上界的理论近似公式,以及最优格距和最优时间步长的理论公式.通过数值算例验证了所得公式的可靠性。然后,发现了两种不同机器精度下最优时间步长之比满足的一个仅与机器精度有关的普适关系.最后,理论验证了在网格比固定的情况下,此问题满足数值计算的不确定性原理,以及在机器有限精度下最优时间步长的必然存在。

A numerical study for some efficient time-integration schemes using barotropic equations

Three kinds of methods, i. e., explicit, semi-implicit, and semi-implicit and semi-Lagrangian method, are tested in the time-integration of shallow-water equations on rotating sphere. Helpful results are available from experiments, especially about the accuracy and efficiency of different semi-implicit and semi-Lagrangian schemes.

ENTROPY CONSISTENCY OF LARGE TIME STEP SCHEMES FOR ISENTROPIC EQUATIONS OF GAS DYNAMICS

In this paper, We show for isentropic equations of gas dynamics with adiabatic exponent gamma=3 that approximations of weak solutions generated by large time step Godunov's scheme or Glimm's scheme give entropy solution in the limit if Courant number is less than or equal to 1.

Design and Analysis of Test Schemes of Static Postponing Time on Shrapnels Used to Riot Control

The test scheme of static postponing time given in our actual national military test standard on shrapnels used to control riot is a nine-point test scheme on the combined action of three kinds of temperatures and three kinds of pressures, the consumed ammunitions are more excessive. Statistic analysis and tentative checkout about a lot of test data are done, feasibility gists are put forward for optimizing of the test design scheme. The optimizing design and data analysis of test scheme of the item are done by managing uniformity design theory, two scientific and reasonable six-point test schemes are confirmed. The feasibility and reliability of the optimizing design schemes put forward above are proved ulteriorly by test validating. The gained schemes not only have good design uniformity and little ammunition wastage and meet the test demand, but also have better forecast ability for the result data of other points using the mathematic models from the actual test points.

RETROSPECTIVE TIME INTEGRAL SCHEME AND ITS APPLICATIONS TO THE ADVECTION EQUATION

To put more information into a difference scheme of a differential equation for making an accurate prediction, a new kind of time integration scheme, known as the retrospective (RT) scheme, is proposed on the basis of the memorial dynamics. Stability criteria of the scheme for an advection equation in certain conditions are derived mathematically. The computations for the advection equation have been conducted with its RT scheme. It is shown that the accuracy of the scheme is much higher than that of the leapfrog (LF) difference scheme.

Times管理方案在心内科护士多参数心电监护仪警报疲劳中的应用

探讨Times管理方案在心内科护士多参数心电监护仪警报疲劳中的应用效果,以提高护士临床警报知识水平,改善警报管理态度和行为,减轻护士的警报疲劳,降低心电监护仪错误警报发生率。

Splitting Based Scheme for Three-dimensional MHD with Dual Time Stepping

A new hybrid numerical scheme of combining an E-CUSP(Energy-Convective Upwind and Split Pressure) method for the fluid part and the Constrained Transport(CT) for the magnetic induction part is proposed.In order to avoid the occurrence of negative pressure in the reconstructed profiles and its updated value,a positivity preserving method is provided.Furthermore,the MHD equations are solved at each physical time step by advancing in pseudo time.The use of dual time stepping is beneficial in the computation since the use of dual time stepping allows the physical time step not to be limited by the corresponding values in the smallest cell and to be selected based on the numerical accuracy criterion.This newly established hybrid scheme combined with positivity preserving method and dual time technique has demonstrated the accurateness and robustness through numerical experiments of benchmark problems such as the 2D Orszag-Tang vortex problem and the3 D shock-cloud interaction problem.

Numerical Study of Fisher’s Equation by Finite Difference Schemes

This research paper represents a numerical approximation to three interesting equations of Fisher, which are linear, non-linear and coupled linear one dimensional reaction diffusion equations from population genetics. We studied accuracy in term of L∞ error norm by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension non-linear reaction diffusion equations.

A New Multidimensional Time Series Forecasting Method Based on the EOF Iteration Scheme

In this paper a new .mnultidimensional time series forecasting scheme based on the empirical orthogonal function (EOF) stepwise iteration process is introduced. The scheme is tested in a series of forecast experiments of Nino3 SST anomalies and Tahiti-Darwin SO index. The results show that the scheme is feasible and ENSO predictable.

Analysis of an Implicit Finite Difference Scheme for Time Fractional Diffusion Equation

Time fractional diffusion equation is usually used to describe the problems involving non-Markovian random walks. This kind of equation is obtained from the standard diffusion equation by replacing the first-order time derivative with a fractional derivative of order α∈(0, 1). In this paper, an implicit finite difference scheme for solving the time fractional diffusion equation with source term is presented and analyzed, where the fractional derivative is described in the Caputo sense. Stability and convergence of this scheme are rigorously established by a Fourier analysis. And using numerical experiments illustrates the accuracy and effectiveness of the scheme mentioned in this paper.

Lagrangian model of zooplankton dispersion:numerical schemes comparisons and parameter sensitivity tests

This paper presents two comparisons or tests for a Lagrangian model of zooplankton dispersion:numerical schemes and time steps.Firstly,we compared three numerical schemes using idealized circulations.Results show that the precisions of the advanced Adams-Bashfold-Moulton(ABM) method and the Runge-Kutta(RK) method were in the same order and both were much higher than that of the Euler method.Furthermore,the advanced ABM method is more efficient than the RK method in computational memory requirements and time consumption.We therefore chose the advanced ABM method as the Lagrangian particle-tracking algorithm.Secondly,we performed a sensitivity test for time steps,using outputs of the hydrodynamic model,Symphonie.Results show that the time step choices depend on the fluid response time that is related to the spatial resolution of velocity fields.The method introduced by Oliveira et al.in 2002 is suitable for choosing time steps of Lagrangian particle-tracking models,at least when only considering advection.

The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect stability.

Nonstandard Numerical Schemes for a Linear Stochastic Oscillator with Additive Noise

In order to simulate a linear stochastic oscillator with additive noise,improved nonstandard optimal(INSOPT) schemes are derived utilizing the nonstandard finite difference(NSFD)technique and the improvement technique.These proposed schemes reproduce long time features of the oscillator solution exactly.Their abilities in preserving the symplecticity,the linear growth property of the second moment and the oscillation property of the solution of the stochastic oscillator system on long time interval are studied.It can be shown that the component { x_n}_(n≥1) of the INSOPT schemes switch signs infinitely many times as n →∞,almost surely.Further,the mean-square convergence order of 1 is obtained for these INSOPT schemes.Finally,numerical experiments illustrate intuitively the results obtained in this paper.

The Stable Explicit Time Stepping Analysis with a New Enrichment Scheme by XFEM

This paper focuses on the study of the stability of explicit time integration algorithm for dynamic problem by the Extended Finite Element Method(XFEM).A new enrichment scheme of crack tip is proposed within the framework of XFEM.Then the governing equations are derived and evolved into the discretized form.For dynamic problem,the lumped mass and the explicit time algorithm are applied.With different grid densities and different forms of Newmark scheme,the Dynamic Stress Intensity Factor(DSIF)is computed by using interaction integral approach to reflect the dynamic response.The effectiveness of the proposed scheme is demonstrated through the numerical examples,and the critical time stepping in different situations are listed and analyzed to illustrate the factors that affect the numerical stability.

Two-Dimensional Nonlinear Reaction Diffusion Equation with Time Efficient Scheme

This research paper represents a numerical approximation to non-linear two-dimensional reaction diffusion equation from population genetics. Since various initial and boundary value problems exist in two-dimensional reaction-diffusion, phenomena are studied numerically by different numerical methods, here we use finite difference schemes to approximate the solution. Accuracy is studied in term of L2, L∞ and relative error norms by random selected grids along time levels for comparison with exact results. The test example demonstrates the accuracy, efficiency and versatility of the proposed schemes. It is shown that the numerical schemes give better solutions. Moreover, the schemes can be easily applied to a wide class of higher dimension nonlinear reaction diffusion equations with a little modification.

LARGE TIME STEP GENERALIZATION OF RANDOM CHOICE FINITE DIFFERENCE SCHEME FOR HYPERBOLIC CONSERVATION LAWS

A natural generalization of random choice finite difference scheme of Harten and Lax for Courant number larger than 1 is obtained. We handle interactions between neighboring Riemann solvers by linear superposition of their conserved quantities. We show consistency of the scheme for arbitrarily large Courant numbers. For scalar problems the scheme is total variation diminishing.A brief discussion is given for entropy condition.

A Compact Finite Volume Scheme for the Multi-Term Time Fractional Sub-Diffusion Equation

In this paper, we introduce high-order finite volume methods for the multi-term time fractional sub-diffusion equation. The time fractional derivatives are described in Caputo’s sense. By using some operators, we obtain the compact finite volume scheme have high order accuracy. We use a compact operator to deal with spatial direction;then we can get the compact finite volume scheme. It is proved that the finite volume scheme is unconditionally stable and convergent in L∞-norm. The convergence order is O(τ2-α + h4). Finally, two numerical examples are given to confirm the theoretical results. Some tables listed also can explain the stability and convergence of the scheme.

Perfect plane-wave source for a high-order symplectic finite-difference time-domain scheme

The method of splitting a plane-wave finite-difference time-domain （SP-FDTD） algorithm is presented for the initiation of plane-wave source in the total-field / scattered-field （TF/SF） formulation of high-order symplectic finite- difference time-domain （SFDTD） scheme for the first time. By splitting the fields on one-dimensional grid and using the nature of numerical plane-wave in finite-difference time-domain （FDTD）, the identical dispersion relation can be obtained and proved between the one-dimensional and three-dimensional grids. An efficient plane-wave source is simulated on one-dimensional grid and a perfect match can be achieved for a plane-wave propagating at any angle forming an integer grid cell ratio. Numerical simulations show that the method is valid for SFDTD and the residual field in SF region is shrinked down to -300 dB.

An efficient locally one-dimensional finite-difference time-domain method based on the conformal scheme

An efficient conformal locally one-dimensional finite-difference time-domain（LOD-CFDTD） method is presented for solving two-dimensional（2D） electromagnetic（EM） scattering problems. The formulation for the 2D transverse-electric（TE） case is presented and its stability property and numerical dispersion relationship are theoretically investigated. It is shown that the introduction of irregular grids will not damage the numerical stability. Instead of the staircasing approximation, the conformal scheme is only employed to model the curve boundaries, whereas the standard Yee grids are used for the remaining regions. As the irregular grids account for a very small percentage of the total space grids, the conformal scheme has little effect on the numerical dispersion. Moreover, the proposed method, which requires fewer arithmetic operations than the alternating-direction-implicit（ADI） CFDTD method, leads to a further reduction of the CPU time. With the total-field/scattered-field（TF/SF） boundary and the perfectly matched layer（PML）, the radar cross section（RCS） of two2 D structures is calculated. The numerical examples verify the accuracy and efficiency of the proposed method.