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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

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自守L-函数集合的零点密度的整体上界估计

数学学报（中文版） 2024年第2期67卷 406-412页

作者：孙海伟叶扬波山东大学数学与统计学院威海264209 爱荷华大学数学系美国爱荷华州爱荷华市52242-1419

本文通过L-函数的整体积分幂矩,来推导某些自守L-函数集合的整体零点密度的上界估计.具体而言,假设I是某些自守表示π构成的集合,对任意π有非负系数c(π)且级数∑_(π∈I)^(c)(π)收敛.假设∑π∈IC(π)∫TT+α|L(2/1+it,π)|2ldt<<εT... 详细信息

本文通过L-函数的整体积分幂矩,来推导某些自守L-函数集合的整体零点密度的上界估计.具体而言,假设I是某些自守表示π构成的集合,对任意π有非负系数c(π)且级数∑_(π∈I)^(c)(π)收敛.假设∑π∈IC(π)∫TT+α|L(2/1+it,π)|2ldt<<εTθ+ε∑π∈IC(π),其中l≥1,0<α≤1,θ≥α.则可以得到整体零点密度∑π∈IC(π)Nπ(σ,T,T+T^(a))的上界估计,这里Nπ(σ,T_(1),T_(2))表示满足σ<β<1及T1≤γ≤T2的L(s,π)的零点ρ=β+iγ的个数.

关键词：零点密度整体零点密度 Riemann zeta-函数自守L-函数积分幂矩整体积分幂矩

表面活性剂辅助分散液相微萃取-气相色谱法分析蔬菜水果中有机磷类农药残留

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分析科学学报 2017年第1期33卷 81-85页

作者：郭伟孙海燕黑龙江八一农垦大学农学院黑龙江大庆163319 黑龙江八一农垦大学测试中心黑龙江大庆163319 农业部农产加工品质量监督检验测试中心黑龙江大庆163319

建立了测定蔬菜水果中有机磷类农药残留的表面活性剂辅助分散液相微萃取-气相色谱法。优化的萃取条件为:在5.0 mL样品溶液中加入50.0μL三氯甲烷和0.5mL 0.04 mmol·L-1的N-十二烷基-β-氨基丙酸盐表面分散剂,分散混匀后,以5 000r·min-... 详细信息

建立了测定蔬菜水果中有机磷类农药残留的表面活性剂辅助分散液相微萃取-气相色谱法。优化的萃取条件为:在5.0 mL样品溶液中加入50.0μL三氯甲烷和0.5mL 0.04 mmol·L-1的N-十二烷基-β-氨基丙酸盐表面分散剂,分散混匀后,以5 000r·min-1离心5min,吸取三氯甲烷相直接进样分析。在最优化条件下,8种有机磷类农药在0.02~0.50μg·mL-1范围内具有良好的线性关系,相关系数在0.9948~0.9985之间;检出限为0.0056~0.0110μg·mL-1。有机磷类农药的富集倍数高达264~537倍。方法应用于蔬菜水果中的有机磷类农药分析,加标回收率在82.4%~114.5%之间;相对标准偏差(RSD)在4.9%~13.7%之间。该方法具有操作简单、富集效率高和灵敏度高等特点,可满足蔬菜水果中有机磷类农药残留的检测。

关键词：表面活性剂分散液相微萃取气相色谱有机磷农药残留

N-苯基-2-萘胺和邻苯二甲酸对生菜内源激素及碳氮代谢的影响

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植物生理学报 2017年第2期53卷 273-279页

作者：郭伟孙海燕王炎黑龙江八一农垦大学农学院/寒地作物种质改良与栽培重点实验室黑龙江大庆163319 黑龙江八一农垦大学测试中心黑龙江大庆163319 哈尔滨工业大学化工与化学学院哈尔滨150001

为明确辣椒(Capsicum annuum)根系分泌的潜在化感物质对生菜(Lactuca sativa)幼苗内源激素及碳氮代谢的影响,分别采用5、10、15、20和25μg·m L^(-1)的N-苯基-2-萘胺(P2NA)和邻苯二甲酸(PA)与1/2Hoagland营养液混合胁迫处理生菜幼苗,... 详细信息

为明确辣椒(Capsicum annuum)根系分泌的潜在化感物质对生菜(Lactuca sativa)幼苗内源激素及碳氮代谢的影响,分别采用5、10、15、20和25μg·m L^(-1)的N-苯基-2-萘胺(P2NA)和邻苯二甲酸(PA)与1/2Hoagland营养液混合胁迫处理生菜幼苗,测定可溶性蛋白质、可溶性糖、内源激素含量以及碳氮代谢关键酶活性,以期丰富辣椒根系分泌物化感机制研究。结果表明:随着化感物质浓度的增加,生菜幼苗根系长度显著降低,根系活力提高;叶片可溶性蛋白质含量逐渐增加,而谷氨酰氨合成酶(GS)活性逐渐降低;蔗糖磷酸合成酶(SPS)活性、蔗糖合酶(SS)活性和可溶性糖含量随着处理浓度的增加呈单峰曲线分布;在0~15μg·m L^(-1)浓度范围内,随着处理浓度的增加,生长素(IAA)和赤霉素(GA)含量逐渐降低,脱落酸(ABA)含量逐渐增加,超过15μg·m L^(-1),结果相反。PA处理的ABA含量和碳代谢活性高于P2NA处理,两者的内源激素含量存在显著的互作效应,而碳、氮代谢和鲜重互作不显著。20和25μg·m L^(-1)的PA和P2NA处理增加了生菜鲜重。影响ABA和GA含量可能是P2NA和PA引起生菜幼苗化感效应的一个重要途径。

关键词：辣椒根系分泌物化感作用碳代谢氮代谢植物激素