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Construction of a Computational Scheme for the Fuzzy HIV/AIDS Epidemic Model with a Nonlinear Saturated Incidence Rate 被引量:1
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作者 Muhammad Shoaib Arif Kamaleldin Abodayeh Yasir Nawaz 《Computer Modeling in Engineering & Sciences》 SCIE EI 2024年第2期1405-1425,共21页
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 epidemi... 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. 展开更多
关键词 Epidemic model fuzzy rate parameters next generation matrix local stability proposed numerical scheme
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Stabilized seventh-order dissipative compact scheme for two-dimensional Euler equations 被引量:1
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作者 Jia-Xian Qin Ya-Ming Chen Xiao-Gang Deng 《Chinese Physics B》 SCIE EI CAS CSCD 2019年第10期408-416,共9页
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 ch... 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. 展开更多
关键词 compact scheme time stability simultaneous APPROXIMATION TERM interface treatment
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Semi-Implicit Scheme to Solve Allen-Cahn Equation with Different Boundary Conditions
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作者 Banan Alqanawi Musa Adam Aigo 《American Journal of Computational Mathematics》 2023年第1期122-135,共14页
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 o... 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. 展开更多
关键词 semi-implicit schemes Allen-Cahn Equations Finite Difference Sparse System Jacobi Fixed Point GAUSS-SEIDEL
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Stabilized seventh-order dissipative compact scheme using simultaneous approximation terms
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作者 Jiaxian QIN Yaming CHEN Xiaogang DENG 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI CSCD 2019年第6期823-836,共14页
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 ra... 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. 展开更多
关键词 HIGH-ORDER scheme compact scheme time stability simultaneous approximation TERM (SAT)
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Stability of Semi-implicit Finite Volume Scheme for Level Set Like Equation
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作者 Kim Kwang-il Son Yong-chol Ma Fu-ming 《Communications in Mathematical Research》 CSCD 2015年第4期351-361,共11页
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 equati... 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. 展开更多
关键词 level set like equation semi-implicit finite volume scheme stabilITY
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Crank-Nicolson Quasi-Compact Scheme for the Nonlinear Two-Sided Spatial Fractional Advection-Diffusion Equations
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作者 Dechao Gao Zeshan Qiu +1 位作者 Lizan Wang Jianxin Li 《Journal of Applied Mathematics and Physics》 2024年第4期1089-1100,共12页
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 oper... 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 L<sub>2</sub>-norm are proved, and the convergence order is . Some examples are given to show that our numerical scheme is effective. 展开更多
关键词 Crank-Nicolson Quasi-Compact scheme Fractional Advection-Diffusion Equations NONLINEAR stability and Convergence
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An Explicit Difference Scheme with High Accuracy and Branching Stability for Solving Parabolic Partial Differential Equation 被引量:4
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作者 马明书 王肖凤 《Chinese Quarterly Journal of Mathematics》 CSCD 2000年第4期98-103,共6页
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+△... 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. 展开更多
关键词 parabolic type equation explicit difference scheme high accuracy branching stability truncation er
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A new scheme of fully stabilized soliton microcombs
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作者 Gui-Lu Long 《Science China(Physics,Mechanics & Astronomy)》 SCIE EI CAS CSCD 2024年第2期1-1,共1页
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^([... 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. 展开更多
关键词 SOLITON stabilized scheme
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Stability of Difference Schemes with Intrinsic Parallelism for Quasilinear Parabolic Systems 被引量:10
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作者 Zhou Yulin and Yuan GuangweiLaboratory of Computational PhysicsCentre for Nonlinear Studies(Institute of Applied Physics and Computational MathematicsP. O. Box 8009, Boiling, 100088, China) 《Wuhan University Journal of Natural Sciences》 CAS 1996年第Z1期579-592,共14页
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... 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. 展开更多
关键词 Difference scheme Intrinsic parallelism Quasilinear 'parabolic systems stability.
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The Stability Research for the Finite Difference Scheme of a Nonlinear Reaction-diffusion Equation 被引量:6
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作者 XU Chen-mei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第2期222-227,共6页
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 differ... 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. 展开更多
关键词 reaction-diffusion equation finite difference scheme stability research variational approximation method
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A High-order Accuracy Explicit Difference Scheme with Branching Stability for Solving Higher-dimensional Heat-conduction Equation 被引量:3
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作者 MA Ming-shu MA Ju-yi +1 位作者 GU Shu-min ZHU Lin-lin 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期446-452,共7页
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 truncatio... 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). 展开更多
关键词 heat-conduction equation explicit difference scheme high-order accuracy branching stability
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A SIMPLE PROOF OF STABILITY AND CONVERGENCE IN L_2 FOR SOME DIFFERENCE SCHEMES AND THEIR EXTRAPOLATION METHOD FOR PARABOLIC EQUATIONS 被引量:1
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作者 孙志忠 《Journal of Southeast University(English Edition)》 EI CAS 1994年第2期1-6,共6页
ASIMPLEPROOFOFSTABILITYANDCONVERGENCEINL_2FORSOMEDIFFERENCESCHEMESANDTHEIREXTRAPOLATIONMETHODFORPARABOLICEQU... ASIMPLEPROOFOFSTABILITYANDCONVERGENCEINL_2FORSOMEDIFFERENCESCHEMESANDTHEIREXTRAPOLATIONMETHODFORPARABOLICEQUATIONSSunZhizhong... 展开更多
关键词 simpld PROOF Wabelic equatiuns DIFFERENCE schemeS stabilITY convergenee EXTRAPOLATION METHOD
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Stability analysis of open-pit gold mine slopes and optimization of mining scheme in Inner Mongolia,China 被引量:2
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作者 REN Shu-lin TAO Zhi-gang +3 位作者 HE Man-chao PANG Shi-hui LI Meng-nan XU Hao-tian 《Journal of Mountain Science》 SCIE CSCD 2020年第12期2997-3011,共15页
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,beddi... 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. 展开更多
关键词 Open pit mine Slope stability Numerical simulation Excavation scheme
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Computational Stability of the Explicit Difference Schemes of the Forced Dissipative Nonlinear Evolution Equations 被引量:1
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作者 林万涛 季仲贞 王斌 《Advances in Atmospheric Sciences》 SCIE CAS CSCD 2001年第3期413-417,共5页
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 ... 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). 展开更多
关键词 Computational quasi-stability Computational stability Forced dissipative nonlinear evolution equation Explicit difference scheme
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Improving the Stability Problem of the Finite Difference Scheme for Reaction-diffusion Equation 被引量:2
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作者 XU Chen-mei 《Chinese Quarterly Journal of Mathematics》 CSCD 北大核心 2008年第3期403-408,共6页
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
关键词 reaction-diffusion equation difference scheme stability problem incremental unknowns
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Stability analysis of slope in strain-softening soils using local arc-length solution scheme 被引量:2
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作者 WANG Xiang-rong RONG Qi-guo +1 位作者 SUN Shu-li WANG Hui 《Journal of Mountain Science》 SCIE CSCD 2017年第1期175-187,共13页
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... 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. 展开更多
关键词 Strain-softening Progressive failure Slope stability Local arc-length scheme Numerical simulation
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IMPROVEMENT ON STABILITY AND CONVERGENCE OF A. D. I. SCHEMES
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作者 程爱杰 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1999年第1期76-83,共8页
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 pa... 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. 展开更多
关键词 P-R scheme Douglas scheme parabolic partial differential equation variable coefficient H-1 energy estimating method stability and convergence
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THE STABILITY OF DIFFERENCE SCHEMES OF A HIGHER DIMENSIONAL PARABOLIC EQUATION
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作者 孙其仁 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 1991年第12期1209-1215,共7页
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 nume... 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. 展开更多
关键词 stability condition parabolic equation difference scheme
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A FAMILY OF HIGH-ORDER ACCURACY EXPLICIT DIFFERENCE SCHEMES WITH BRANCHING STABILITY FOR SOLVING 3-D PARABOLIC PARTIAL DIFFERENTIAL EQUATION
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作者 马明书 王同科 《Applied Mathematics and Mechanics(English Edition)》 SCIE EI 2000年第10期1207-1212,共6页
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 t... 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)). 展开更多
关键词 high-order accuracy explicit difference scheme branching stability 3-D parabolic PDE
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Stability of High-Order Staggered-Grid Schemes for 3D Elastic Wave Equation in Heterogeneous Media
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作者 Atish Kumar Joardar Wensheng Zhang 《Journal of Applied Mathematics and Physics》 2019年第8期1755-1774,共20页
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 plan... 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. 展开更多
关键词 3D ELASTIC Wave INHOMOGENEOUS Media Staggered-Grid scheme HIGH-ORDER stabilITY Energy ESTIMATE
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