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A FAST COMPACT DIFFERENCE METHOD FOR TWO-DIMENSIONAL NONLINEAR SPACE-FRACTIONAL COMPLEX GINZBURG-LANDAU EQUATIONS

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Journal of Computational Mathematics 2021年第5期39卷 708-732页

作者： Lu Zhang Qifeng Zhang hai-wei sun School of Mathematics and Statistics Xuzhou University of TechnologyXuzhou 221018China Department of Mathematics Zhejiang Sci-Tech UniversityHangzhou 310018China Department of Mathematics University of MacaoMacaoChina

This paper focuses on a fast and high-order finite difference method for two-dimensional space-fractional complex Ginzburg-Landau *** firstly establish a three-level finite difference scheme for the time variable,followed by the linearized technique of the nonlinear *** the fourth-order compact finite difference method is employed to discretize the spatial *** the accuracy of the discretization is O(τ^(2)+h^(4)_(1)+h^(4)_(2))in L_(2)-norm,where τ is the temporal step-size,both h_(1) and h_(2) denote spatial mesh sizes in x-and y-directions,*** rigorous theoretical analysis,including the uniqueness,the almost unconditional stability,and the convergence,is studied via the energy ***,the discretized system holds the block Toeplitz ***,the coefficient Toeplitz-like matrix only requires O(M_(1)M_(2)) memory storage,and the matrix-vector multiplication can be carried out in O(M_(1)M_(2))(log M_(1)+log M_(2))computational complexity by the fast Fourier transformation,where M_(1) and M_(2) denote the numbers of the spatial grids in two different *** order to solve the resulting Toeplitz-like system quickly,an efficient preconditioner with the Krylov subspace method is proposed to speed up the iteration *** results are given to demonstrate the well performance of the proposed method.

关键词： Space-fractional Ginzburg-Landau equation Compact scheme Boundedness Convergence Preconditioner FFT

Asymptotic Stability of an Eikonal Transformation Based ADI Method for the Paraxial Helmholtz Equation at High Wave Numbers

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Communications in Computational Physics 2012年第9期12卷 1275-1292页

作者： Qin Sheng hai-wei sun Center for Astrophysics Space Physics and Engineering ResearchDepartment of MathematicsBaylor UniversityWacoTX 76798-7328USA Department of Mathematics University of MacaoMacao

This paper concerns the numerical stability of an eikonal transformation based splitting method which is highly effective and efficient for the numerical solution of paraxial Helmholtz equation with a large wave *** matrix analysis is conducted in investigations and the oscillation-free computational procedure is proven to be stable in an asymptotic *** examples are given to illustrate the conclusion.

关键词： Paraxial equation highly oscillatory problems eikonal splitting asymptotic stability matrix eigenvalues spectral radius

Fast Second-Order Evaluation for Variable-Order Caputo Fractional Derivative with Applications to Fractional Sub-Diffusion Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第1期15卷 200-226页

作者： Jia-Li Zhang Zhi-wei Fang hai-wei sun Department of Mathematics University of MacaoMacaoSARChina

In this paper,we propose a fast second-order approximation to the variable-order(VO)Caputo fractional derivative,which is developed based on L2-1σformula and the exponential-sum-approximation *** fast evaluation method can achieve the second-order accuracy and further reduce the computational cost and the acting memory for the VO Caputo fractional *** fast algorithm is applied to construct a relevant fast temporal second-order and spatial fourth-order scheme(F L2-1σscheme)for the multi-dimensional VO time-fractional sub-diffusion ***,F L2-1σscheme is proved to fulfill the similar properties of the coefficients as those of the well-studied L2-1σ***,F L2-1σscheme is strictly proved to be unconditionally stable and convergent.A sharp decrease in the computational cost and the acting memory is shown in the numerical examples to demonstrate the efficiency of the proposed method.

关键词： Variable-order Caputo fractional derivative exponential-sum-approximation method fast algorithm time-fractional sub-diffusion equation stability and convergence

Fourth Order Compact Boundary Value Method for Option Pricing with Jumps

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Advances in Applied Mathematics and Mechanics 2009年第6期1卷 845-861页

作者： Spike T.Lee hai-wei sun Department of Mathematics University of MacaoMacaoChina

We consider pricing options in a jump-diffusion model which requires solving a partial integro-differential *** the spatial direction with a fourth order compact scheme leads to a linear system of ordinary differential *** the temporal direction,we utilize the favorable boundary value methods owing to their advantageous stability *** addition,the resulting large sparse system can be solved rapidly by the GMRES method with a circulant Strang-type *** results demonstrate the high order accuracy of our scheme and the efficiency of the preconditioned GMRES method.

关键词： Partial integro-differential equation fourth order compact scheme boundary value method preconditioning Toeplitz matrix

Spectral Analysis for Preconditioning of Multi-Dimensional Riesz Fractional Diffusion Equations

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Numerical Mathematics(Theory,Methods and Applications) 2022年第3期15卷 565-591页

作者： Xin Huang Xue-Lei Lin Michael K.Ng hai-wei sun Department of Mathematics University of MacaoMacao SARChina Shenzhen JL Computational Science and Applied Research Institute Shenzhen 518131China Beijing Computational Science Research Center Beijing 100193China Department of Mathematics The University of HongkongHong Kong SARChina

In this paper,we analyze the spectra of the preconditioned matrices arising from discretized multi-dimensional Riesz spatial fractional diffusion *** finite difference method is employed to approximate the multi-dimensional Riesz fractional derivatives,which generates symmetric positive definite ill-conditioned multi-level Toeplitz *** preconditioned conjugate gradient method with a preconditioner based on the sine transform is employed to solve the resulting linear ***,we prove that the spectra of the preconditioned matrices are uniformly bounded in the open interval(12,32)and thus the preconditioned conjugate gradient method converges linearly within an iteration number independent of the discretization ***,the proposed method can be extended to handle ill-conditioned multi-level Toeplitz matrices whose blocks are generated by functions with zeros of fractional *** theoretical results fill in a vacancy in the *** examples are presented to show the convergence performance of the proposed preconditioner that is better than other preconditioners.

关键词： Multi-dimensional Riesz fractional derivative multi-level Toeplitz matrix sine transform based preconditioner preconditioned conjugate gradient method

An Efficient Second-Order Convergent Scheme for One-Side Space Fractional Diffusion Equations with Variable Coefficients

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Communications on Applied Mathematics and Computation 2020年第2期2卷 215-239页

作者： Xue-lei Lin Pin Lyu Michael KNg hai-wei sun Seakweng Vong Department of Mathematics Hong Kong Baptist UniversityHong KongChina School of Economic Mathematics Southwestern University of Finance and EconomicsChengdu 611130China Department of Mathematics The University of Hong KongHong KongChina Department of Mathematics University of MacaoMacaoChina

In this paper,a second-order fnite-diference scheme is investigated for time-dependent space fractional difusion equations with variable *** the presented scheme,the Crank-Nicolson temporal discretization and a second-order weighted-and-shifted Grünwald-Letnikov spatial discretization are ***,the unconditional stability and the second-order convergence in time and space of the proposed scheme are established under some conditions on the variable ***,a Toeplitz preconditioner is proposed for linear systems arising from the proposed *** condition number of the preconditioned matrix is proven to be bounded by a constant independent of the discretization step-sizes,so that the Krylov subspace solver for the preconditioned linear systems converges *** results are reported to show the convergence rate and the efciency of the proposed scheme.

关键词： One-side space fractional difusion equation Variable difusion coefcients Stability and convergence High-order fnite-diference scheme Preconditioner

A dual measurement method of strain and temperature

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Journal of Marine Science and Application 2007年第1期6卷 63-68页

作者： JIANG hai-li sun wei-min ZHANG Cong LIU Zhi-hai JIANG Fu-qiang ZHANG Yang College of Science Harbin Engineering University Harbin 150001 China

With the rapid development of China's foreign trade, the coastal and inland waterway transport has been increased rapidly. The potential market for marine engines is more and more obvious. The measurement of the engine temperature and strain becomes very important. The fluorescence fiber sensors are broadly used to measure temperature, concentration, and pH value, etc. The fluorescence sensing systems are based on different principles, namely fluorescence intensity, fluorescence intensity ratio, and fluorescence lifetime. The fluorescence lifetime is an effective parameter for sensing purpose, because it is independent of the intensity of the pumping source and does not need expensive narrow-band filters. An experiment system has been established, in which some samples were produced to measure the fluorescence lifetime and temperature characteristics and the relationship of the strain and temperature versus the fluorescence lifetime was achieved at the same time. The experiment result was fitted and analyzed. The test results show that the fluorescence lifetime decreases with the increasing of temperature. The change of fluorescence lifetime with the strain is inconspicuous comparing to that with the temperature.

关键词： fluorescence lifetime fluorescence fiber simultaneous measurement temperature strain

Negative efficacy of antidepressants in pharmacotherapy of child and adolescent depression

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World Journal of Psychiatry 2025年第1期15卷 32-36页

作者： Min Xu hai-Ying Jin Feng-Li sun wei-Dong Jin Department of Psychiatry Zhejiang Chinese Medical UniversityHangzhou 310053Zhejiang ProvinceChina Department of Psychiatry Tongde Hospital of Zhejiang ProvinceHangzhou 310012Zhejiang ProvinceChina Department of Psychiatry Zhejiang Provincial Mental Health CenterHangzhou 311122Zhejiang ProvinceChina

Antidepressants are the main drugs used to treat depression,but they have not been shown to be effective in the treatment of child and adolescent ***,many adolescent depression treatment guidelines still recommend the use of antidepressants,especially specific serotonin re-uptake *** studies have suggested that antidepressants have little therapeutic effect but many side effects,such as switching to mania,suicide,and non-suicidal self injury(NSSI),in the treatment of child and adolescent *** the process of developing guidelines,drug recommendations should not only focus on impro-ving symptoms,but they should also consider potential side *** review discusses the serious side effects of antidepressants,including switching to mania,suicide,and NSSI.

关键词： Child depression Adolescent depression Antidepressant Switch Suicide Non-suicidal self injury

Observer-based event-triggered formation tracking control for second-order multi-agent systems in constrained region

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Science China(Information Sciences) 2025年第2期68卷 151-169页

作者： Fenglan sun Zhonghua XU wei ZHU ■ KURTHS Key Lab of Intelligent Analysis and Decision on Complex Systems School of ScienceChongqing University of Posts and Telecommunications Key Lab of Intelligent Air-Ground Cooperative Control for Universities in Chongqing College of AutomationChongqing University of Posts and Telecommunications Department of Complexity Science Potsdam Institute for Climate Impact Research Institute of Physics Humboldt University of Berlin

In this paper, an event-triggered time-varying formation tracking control for a class of second-order nonlinear multiagent systems(MAS) operating within a constrained region is investigated. To mitigate the negative effects of external unknown disturbance, a novel disturbance observer with performance guarantees is proposed, enabling precise disturbance *** the artificial potential field(APF) method, a repulsive potential function is introduced to prevent inter-agent collisions as well as collisions with environmental obstacles. To reduce continuous communication and frequent system updates, a sliding mode technique is incorporated into the formation tracking controller, utilizing an event-triggered mechanism. The controller is also applicable to the formation control of MAS in switching-constrained regions. The achievement of the specified timevarying geometric formation is rigorously demonstrated through the Lyapunov framework. Numerical simulations are presented to validate the effectiveness of the theoretical results.

关键词： formation tracking control region constraints repulsive potential function event-triggered mechanism