Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate

This work aimed to construct an epidemic model with fuzzy parameters.Since the classical epidemic model doesnot elaborate on the successful interaction of susceptible and infective people,the constructed fuzzy epidemicmodel discusses the more detailed versions of the interactions between infective and susceptible people.Thenext-generation matrix approach is employed to find the reproduction number of a deterministic model.Thesensitivity analysis and local stability analysis of the systemare also provided.For solving the fuzzy epidemic model,a numerical scheme is constructed which consists of three time levels.The numerical scheme has an advantage overthe existing forward Euler scheme for determining the conditions of getting the positive solution.The establishedscheme also has an advantage over existing non-standard finite difference methods in terms of order of accuracy.The stability of the scheme for the considered fuzzy model is also provided.From the plotted results,it can beobserved that susceptible people decay by rising interaction parameters.

Stabilized seventh-order dissipative compact scheme for two-dimensional Euler equations

We derive in this paper a time stable seventh-order dissipative compact finite difference scheme with simultaneous approximation terms(SATs) for solving two-dimensional Euler equations. To stabilize the scheme, the choice of penalty coefficients for SATs is studied in detail. It is demonstrated that the derived scheme is quite suitable for multi-block problems with different spacial steps. The implementation of the scheme for the case with curvilinear grids is also discussed.Numerical experiments show that the proposed scheme is stable and achieves the design seventh-order convergence rate.

Semi-Implicit Scheme to Solve Allen-Cahn Equation with Different Boundary Conditions

The aim of this paper is to give an appropriate numerical method to solve Allen-Cahn equation, with Dirichlet or Neumann boundary condition. The time discretization involves an explicit scheme for the nonlinear part of the operator and an implicit Euler discretization of the linear part. Finite difference schemes are used for the spatial part. This finally leads to the numerical solution of a sparse linear system that can be solved efficiently.

Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms

To ensure time stability of a seventh-order dissipative compact finite difference scheme, fourth-order boundary closures are used near domain boundaries previously. However, this would reduce the global convergence rate to fifth-order only. In this paper, we elevate the boundary closures to sixth-order to achieve seventh-order global accuracy. To keep the improved scheme time stable, the simultaneous approximation terms (SATs) are used to impose boundary conditions weakly. Eigenvalue analysis shows that the improved scheme is time stable. Numerical experiments for linear advection equations and one-dimensional Euler equations are implemented to validate the new scheme.

Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation

We study numerical methods for level set like equations arising in image processing and curve evolution problems. Semi-implicit finite volume-element type schemes are constructed for the general level set like equation （image selective smoothing model） given by Alvarez et al. （Alvarez L, Lions P L, Morel J M. Image selective smoothing and edge detection by nonlinear diffusion II. SIAM J. Numer. Anal., 1992, 29： 845-866）. Through the reasonable semi-implicit discretization in time and co-volume method for space approximation, we give finite volume schemes, unconditionally stable in L∞ and W1＇2 （W1＇1） sense in isotropic （anisotropic） diffu- sion domain.

Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations

The higher-order numerical scheme of nonlinear advection-diffusion equations is studied in this article, where the space fractional derivatives are evaluated by using weighted and shifted Grünwald difference operators and combining the compact technique, in the time direction is discretized by the Crank-Nicolson method. Through the energy method, the stability and convergence of the numerical scheme in the sense of L2-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective.

An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation

This paper presents an explicit difference scheme with accuracy and branching stability for solving onedimensional parabolic type equation by the method of undetermined parameters and its truncation error is O(△t4+△x4). The stability condition is r=a△t/△x2<1/2.

A new scheme of fully stabilized soliton microcombs

More stable frequency standard has been the focus of studies for a long time^([1,2]).Dissipative Kerr solitons(DKSs)in microresonators have attracted much interest for their potential in on-chip frequency standards^([1]).DKSs provide frequency combs characterized by high coherence,expansive bandwidth,and microwave-repetition rates.

Stability of Difference Schemes with Intrinsic Parallelism for Quasilinear Parabolic Systems

In this paper, the first boundary problem of quasilinear parabolic system of second order is studied by the finite difference method with intrinsic parallelism. for the problem, the stability of the difference schemes with intrinsic parallelism are justified in the sense of the continuous dependence of the discrete vector solution of the difference schemes on the discrete data of the original problem, without assuming the existence of the smooth solutions for the origillal problem.

The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation

In the article, the fully discrete finite difference scheme for a type of nonlinear reaction-diffusion equation is established. Then the new function space is introduced and the stability problem for the finite difference scheme is discussed by means of variational approximation method in this function space. The approach used is of a simple characteristic in gaining the stability condition of the scheme.

A High-order Accuracy Explicit Difference Scheme with Branching Stability for Solving Higher-dimensional Heat-conduction Equation

A high-order accuracy explicit difference scheme for solving 4-dimensional heatconduction equation is constructed. The stability condition is r = △t/△x^2 = △t/△y^2 = △t/△z^2 = △t/△w^2 〈 3/8, and the truncation error is O（△t^2 ＋ △x^4）.

A SIMPLE PROOF OF STABILITY AND CONVERGENCE IN L＿2 FOR SOME DIFFERENCE SCHEMES AND THEIR EXTRAPOLATION METHOD FOR PARABOLIC EQUATIONS

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Stability analysis of open-pit gold mine slopes and optimization of mining scheme in Inner Mongolia,China

The geological structure of the Changshanhao open-pit mine in Urad Middle Banner,Inner Mongolia,China is extremely complicated,and slope instability has frequently occurred in various forms,such as wedge sliding,bedding sliding,and toppling failure.In order to study the failure mechanisms of these slopes,the geological structure and mechanical rock properties were investigated based on field investigations and laboratory tests.Numerical models for the present mining area and final mining area of the original scheme were established to analyze slope stability.The results showed that the unique geomorphological characteristics of the mining area were generated by geological tectonism,and the north side of the stope is an anti-dip layered rock slope and the south side is a dip layered rock slope.Slope failure is the consequence of endogenic and exogenic integration,including physical and mechanical properties of the rock mass,geological structures such as faults and joints,and human-caused factors such as blasting and excavation disturbances.Then the original excavation scheme was redesigned mainly by optimizing the slope angle and decreasing the final mining depth to maintain slope stability.Finally,the Monte Carlo method was used to analyze the reliability of the slope angle optimization scheme.The open-pit mine excavation plan that meets the stability requirements was obtained eventually.

Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations

The computational stability of the explicit difference schemes of the forced dissipative nonlinear evolution equations is analyzed and the computational quasi-stability criterion of explicit difference schemes of the forced dissipative nonlinear atmospheric equations is obtained on account of the concept of computational quasi-stability, Therefore, it provides the new train of thought and theoretical basis for designing computational stable difference scheme of the forced dissipative nonlinear atmospheric equations. Key words Computational quasi-stability - Computational stability - Forced dissipative nonlinear evolution equation - Explicit difference scheme This work was supported by the National Outstanding Youth Scientist Foundation of China (Grant No. 49825109), the Key Innovation Project of Chinese Academy of Sciences (KZCX1-10-07), the National Natural Science Foundation of China (Grant Nos, 49905007 and 49975020) and the Outstanding State Key Laboratory Project (Grant No. 40023001).

Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation

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.

Stability analysis of slope in strain-softening soils using local arc-length solution scheme

Soils with strain-softening behavior — manifesting as a reduction of strength with increasing plastic strain — are commonly found in the natural environment. For slopes in these soils,a progressive failure mechanism can occur due to a reduction of strength with increasing strain. Finite element method based numerical approaches have been widely performed for simulating such failure mechanism,owning to their ability for tracing the formation and development of the localized shear strain. However,the reliability of the currently used approaches are often affected by poor convergence or significant mesh-dependency,and their applicability is limited by the use of complicated soil models. This paper aims to overcome these limitations by developing a finite element approach using a local arc-length controlled iterative algorithm as the solution strategy. In the proposed finite element approach,the soils are simulated with an elastoplastic constitutive model in conjunction with the Mohr-Coulomb yield function. The strain-softening behavior is represented by a piece-wise linearrelationship between the Mohr-Coulomb strength parameters and the deviatoric plastic strain. To assess the reliability of the proposed finite element approach,comparisons of the numerical solutions obtained by different finite element methods and meshes with various qualities are presented. Moreover,a landslide triggered by excavation in a real expressway construction project is analyzed by the presented finite element approach to demonstrate its applicability for practical engineering problems.

IMPROVEMENT ON STABILITY AND CONVERGENCE OF A. D. I. SCHEMES

Alternating direction implicit (A.D.I.) schemes have been proved valuable in the approximation of the solutions of parabolic partial differential equations in multi-dimensional space. Consider equations in the form partial derivative u/partial derivative t - partial derivative/partial derivative x(a(x,y,t) partial derivative u/partial derivative x) - partial derivative/partial derivative y(b(x,y,t) partial derivative u partial derivative y) = f Two A.D.I. schemes, Peaceman-Rachford scheme and Douglas scheme will be studied. In the literature, stability and convergence have been analysed with Fourier Method, which cannot be extended beyond the model problem with constant coefficients. Additionally, L-2 energy method has been introduced to analyse the case of non-constant coefficients, however, the conclusions are too weak and incomplete because of the so-called 'equivalence between L-2 norm and H-1 semi-norm'. In this paper, we try to improve these conclusions by H-1 energy estimating method. The principal results are that both of the two A.D.I. schemes are absolutely stable and converge to the exact solution with error estimations O(Delta t(2) + h(2)) in discrete H-1 norm. This implies essential improvement of existing conclusions.

THE STABILITY OF DIFFERENCE SCHEMES OF A HIGHER DIMENSIONAL PARABOLIC EQUATION

This paper proposes a new method to improve the stability condition of difference scheme of a parabolic equation. Necessary and sufficient conditions of the stability of this new method are given and proved. Some numerical examples show that this method has some calculation advantages.

A FAMILY OF HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 3-D PARABOLIC PARTIAL DIFFERENTIAL EQUATION

A family of high-order accuracy explict difference schemes for solving 3-dimension parabolic P. D. E. is constructed. The stability condition is r = Deltat/Deltax(2) Deltat/Deltay(2) = Deltat/Deltaz(2) < 1/2 ,and the truncation error is 0(<Delta>t(2) + Deltax(4)).

Stability of High-Order Staggered-Grid Schemes for 3D Elastic Wave Equation in Heterogeneous Media

In this paper, we firstly derive the stability conditions of high-order staggered-grid schemes for the three-dimensional (3D) elastic wave equation in heterogeneous media based on the energy method. Moreover, the plane wave analysis yields a sufficient and necessary stability condition by the von Neumann criterion in homogeneous case. Numerical computations for 3D wave simulation with point source excitation are given.