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MEAN SQUARE STABILITY AND DISSIPATIVITY OF split- step THETA method FOR NONLINEAR NEUTRAL STOCHASTIC DELAY DIFFERENTIAL EQUATIONS WITH POISSON JUMPS

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Journal of Computational Mathematics 2017年第6期35卷 766-779页

作者： Haiyan Yuan Jihong Shen Cheng Song Department of Mathematics Heilongjiang Institute of Technology Harbin 150050 China Department of Mathematics Harbin Engineering University Harbin 150050 China Department of Management Harbin Institute University Harbin 150001 China

In this paper, a split-step 0 （SST） method is introduced and used to solve the non- linear neutral stochastic differential delay equations with Poisson jumps （NSDDEwPJ）. The mean square asymptotic stability of the SST method for nonlinear neutral stochastic differential equations with Poisson jumps is studied. It is proved that under the one-sided Lipschitz condition and the linear growth condition, the SST method with ∈ E （0, 2 -√2） is asymptotically mean square stable for all positive step sizes, and the SST method with ∈ E （2 -√2, 1） is asymptotically mean square stable for some step sizes. It is also proved in this paper that the SST method possesses a bounded absorbing set which is independent of initial data, and the mean square dissipativity of this method is also proved.

关键词： Neutral stochastic delay differential equations split-step method Stability,Poisson jumps.

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High Accuracy split-step Finite Difference method for Schrdinger-KdV Equations

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Communications in Theoretical Physics 2018年第10期70卷 413-422页

作者： Feng Liao Lu-Ming Zhang School of Mathematics and Statistics Changshu Institute of TechnologyChangshu 215500China College of Science Nanjing University of Aeronautics and AstronauticsNanjing 211106China

In this article, two split-step finite difference methods for Schrodinger-KdV equations are formulated and investigated. The main features of our methods are based on:(i) The applications of split-step technique for Schrodingerlike equation in time.(ii) The utilizations of high-order finite difference method for KdV-like equation in spatial discretization.(iii) Our methods are of spectral-like accuracy in space and can be realized by fast Fourier transform efficiently. Numerical experiments are conducted to illustrate the efficiency and accuracy of our numerical methods.

关键词： split-step method SchrSdinger-KdV equations finite difference method fast Fourier transform

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Novel Multi-Symplectic Integrators for Nonlinear Fourth-Order Schrodinger Equation with Trapped Term

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Communications in Computational Physics 2010年第3期7卷 613-630页

作者： Jialin Hong Linghua Kong State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering ComputingAcademy of Mathematics and System ScienceChinese Academy of SciencesP.O.Box 2719Beijing 100190China School of Mathematics and Information Science Jiangxi Normal UniversityNanchangJiangxi 330022China

The multi-symplectic Runge-Kutta (MSRK) methods and multi-symplecticFourier spectral (MSFS) methods will be employed to solve the fourth-orderSchrodinger equations with trapped term. Using the idea of split-step numericalmethod and the MSRK methods, we devise a new kind of multi-symplectic integrators, which is called split-step multi-symplectic (SSMS) methods. The numerical experiments show that the proposed SSMS methods are more efficient than the conventionalmulti-symplectic integrators with respect to the the numerical accuracy and conservation perserving properties.

关键词： Schrodinger equation with trapped term multi-symplectic scheme Fourier spectral method conservation law split-step method

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