This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either...This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.展开更多
In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear conve...In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.展开更多
This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that...This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.展开更多
In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and dec...In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.展开更多
Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of un...Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.展开更多
目的探究高特质焦虑个体认知重评和表达抑制的使用习惯及其在内隐/外显条件下使用2种情绪调节策略的特点。方法于2023年6月至2023年7月招募57名某军医大学非心理学专业本科生或研究生被试。采用特质焦虑量表(Trait form of Spielberger...目的探究高特质焦虑个体认知重评和表达抑制的使用习惯及其在内隐/外显条件下使用2种情绪调节策略的特点。方法于2023年6月至2023年7月招募57名某军医大学非心理学专业本科生或研究生被试。采用特质焦虑量表(Trait form of Spielberger’s State-Trait Anxiety Inventory,STAI-T)和情绪调节问卷(Emotion Regulation Questionnaire,ERQ)对其焦虑水平以及认知重评和表达抑制2种策略的使用习惯进行调查。按照STAI-T得分将其分为高特质焦虑(high trait anxiety,HTA)和低特质焦虑(low trait anxiety,LTA)2组,其中HTA组28例,LTA组29例,并采用内隐和外显情绪调节任务分析比较2种策略对负性情绪愉悦度和唤醒度的改善效果,以及外显条件下2种策略的难度和成功度差异。结果①2组均习惯于使用认知重评,而较少使用表达抑制[t(27)=3.94,P<0.001;t(28)=11.33,P<0.001];相较于LTA个体,HTA个体表达抑制的使用频率更高[t(55)=3.02,P<0.01],而认知重评的使用频率较低[t(55)=-2.20,P=0.02];②内隐条件下,相对于中性启动,认知重评(愉悦度:2.56±0.11 vs 2.73±0.12,P<0.01;唤醒度:6.68±0.18 vs 6.51±0.20,P<0.05)和表达抑制启动(愉悦度:2.56±0.11 vs 2.86±0.11,P<0.001;唤醒度:6.68±0.18 vs 6.30±0.20,P<0.001)都可改善2组被试的负性情绪体验,且表达抑制的效果更好(愉悦度:P<0.001,唤醒度:P<0.001)。③外显条件下,认知重评(愉悦度:2.92±0.12 vs 5.09±0.09,P<0.001;唤醒度:6.43±0.20 vs 4.33±0.21,P<0.001)和表达抑制(愉悦度:2.92±0.12 vs 4.34±0.09,P<0.001;唤醒度:6.43±0.20 vs 4.22±0.22,P<0.001)均可显著改善HTA和LTA个体的负性情绪体验,且认知重评对愉悦度的提升优于表达抑制(P<0.001);不同特质焦虑水平间比较显示HTA个体对两种情绪调节策略的使用均显得更为困难[认知重评:t(55)=2.16,P=0.02;表达抑制:t(55)=2.92,P<0.01],且表达抑制的情绪调节成功度更低[t(55)=-1.88,P=0.03];对HTA个体自身而言,使用表达抑制的难度要大于认知重评[4.00±1.81 vs 5.00±1.80,t(27)=-2.78,P<0.01],且成功度更低[7.04±1.00 vs 6.64±1.13,t(27)=2.09,P=0.02]。④比较内隐和外显条件下的情绪调节效应,发现高、低特质焦虑个体外显情绪调节对愉悦度(外显重评vs内隐重评:5.09±0.09 vs 2.73±0.12,P<0.001;外显抑制vs内隐抑制:4.34±0.09 vs 2.86±0.11,P<0.001)和唤醒度(外显重评vs内隐重评:4.33±0.21 vs 6.51±0.20,P<0.001;外显抑制vs内隐抑制:4.22±0.22 vs 6.30±0.20,P<0.001)的改善效果均优于内隐条件。结论高特质焦虑个体存在认知重评使用相对不足、表达抑制使用偏多的特点;在内隐和外显条件下,认知重评和表达抑制均能有效改善高特质焦虑个体的负性情绪体验,且外显情绪调节的效果均优于内隐。展开更多
尽管从方法运用角度对文史文本深度翻译的探讨已经相当丰富,但在实施深度翻译方法之前,确立指导原则的重要性仍然不容忽视。这些原则为文史文本深度翻译实践提供了指导和规范,确保了深度翻译的准确性和一致性,并具有更广泛的适用性。在...尽管从方法运用角度对文史文本深度翻译的探讨已经相当丰富,但在实施深度翻译方法之前,确立指导原则的重要性仍然不容忽视。这些原则为文史文本深度翻译实践提供了指导和规范,确保了深度翻译的准确性和一致性,并具有更广泛的适用性。在翻译威尔森的英国通俗史畅销书《后维多利亚时代人》(After the Victorians)中,笔者较多地运用了阿皮亚最早提出的深度翻译方法,采用的具体分类是曹明伦提出的显性深度翻译和隐性深度翻译。本文将对曹明伦重新归纳出的显性深度翻译与隐性深度翻译的方法做一简要介绍,包括隐性深度翻译的提出过程,然后重点结合笔者翻译《后维多利亚时代人》的实践,讨论一般史学著作深度翻译应遵循的原则。在讨论中,本文将涵盖上述两种深度翻译方法的操作与例析。展开更多
It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which ...It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.展开更多
基金supported by the NSF under Grant DMS-2208391sponsored by the NSF under Grant DMS-1753581.
文摘This paper provides a study on the stability and time-step constraints of solving the linearized Korteweg-de Vries(KdV)equation,using implicit-explicit(IMEX)Runge-Kutta(RK)time integration methods combined with either finite difference(FD)or local discontinuous Galerkin(DG)spatial discretization.We analyze the stability of the fully discrete scheme,on a uniform mesh with periodic boundary conditions,using the Fourier method.For the linearized KdV equation,the IMEX schemes are stable under the standard Courant-Friedrichs-Lewy(CFL)conditionτ≤λh.Here,λis the CFL number,τis the time-step size,and h is the spatial mesh size.We study several IMEX schemes and characterize their CFL number as a function ofθ=d/h^(2)with d being the dispersion coefficient,which leads to several interesting observations.We also investigate the asymptotic behaviors of the CFL number for sufficiently refined meshes and derive the necessary conditions for the asymptotic stability of the IMEX-RK methods.Some numerical experiments are provided in the paper to illustrate the performance of IMEX methods under different time-step constraints.
基金the NSFC grant 11871428the Nature Science Research Program for Colleges and Universities of Jiangsu Province grant 20KJB110011Qiang Zhang:Research supported by the NSFC grant 11671199。
文摘In this paper,a fully discrete stability analysis is carried out for the direct discontinuous Galerkin(DDG)methods coupled with Runge-Kutta-type implicit-explicit time marching,for solving one-dimensional linear convection-diffusion problems.In the spatial discretization,both the original DDG methods and the refined DDG methods with interface corrections are considered.In the time discretization,the convection term is treated explicitly and the diffusion term implicitly.By the energy method,we show that the corresponding fully discrete schemes are unconditionally stable,in the sense that the time-stepis only required to be upper bounded by a constant which is independent of the mesh size h.Opti-mal error estimate is also obtained by the aid of a special global projection.Numerical experiments are given to verify the stability and accuracy of the proposed schemes.
文摘This paper considers pricing European options under the well-known of SVJ model of Bates and related computational methods. According to the no-arbitrage principle, we first derive a partial differential equation that the value of any European contingent claim should satisfy, where the asset price obeys the SVJ model. This equation is numerically solved by using the implicit- explicit backward difference method and time semi-discretization. In order to explain the validity of our method, the stability of time semi-discretization scheme is also proved. Finally, we use a simulation example to illustrate the efficiency of the method.
基金supported by National Natural Science Foundation of China(Grant No.11801569)Natural Science Foundation of Shandong Province(CN)(Grant No.ZR2021MA001)the Fundamental Research Funds for the Central Universities(Grant Nos.22CX03025A and 22CX03020A).
文摘In this paper,two fully-discrete local discontinuous Galerkin(LDG)methods are applied to the growth-mediated autochemotactic pattern formation model in self-propelling bacteria.The numerical methods are linear and decoupled,which greatly improve the computational efficiency.In order to resolve the time level mismatch of the discretization process,a special time marching method with high-order accuracy is constructed.Under the condition of slight time step constraints,the optimal error estimates of this method are given.Moreover,the theoretical results are verified by numerical experiments.Real simulations show the patterns of spots,rings,stripes as well as inverted spots because of the interplay of chemotactic drift and growth rate of the cells.
基金supported by the National Natural Science Foundation of China(No.92252201)the Fundamental Research Funds for the Central Universitiesthe Academic Excellence Foundation of Beihang University(BUAA)for PhD Students。
文摘Efficient and accurate simulation of unsteady flow presents a significant challenge that needs to be overcome in computational fluid dynamics.Temporal discretization method plays a crucial role in the simulation of unsteady flows.To enhance computational efficiency,we propose the Implicit-Explicit Two-Step Runge-Kutta(IMEX-TSRK)time-stepping discretization methods for unsteady flows,and develop a novel adaptive algorithm that correctly partitions spatial regions to apply implicit or explicit methods.The novel adaptive IMEX-TSRK schemes effectively handle the numerical stiffness of the small grid size and improve computational efficiency.Compared to implicit and explicit Runge-Kutta(RK)schemes,the IMEX-TSRK methods achieve the same order of accuracy with fewer first derivative calculations.Numerical case tests demonstrate that the IMEX-TSRK methods maintain numerical stability while enhancing computational efficiency.Specifically,in high Reynolds number flows,the computational efficiency of the IMEX-TSRK methods surpasses that of explicit RK schemes by more than one order of magnitude,and that of implicit RK schemes several times over.
文摘目的探究高特质焦虑个体认知重评和表达抑制的使用习惯及其在内隐/外显条件下使用2种情绪调节策略的特点。方法于2023年6月至2023年7月招募57名某军医大学非心理学专业本科生或研究生被试。采用特质焦虑量表(Trait form of Spielberger’s State-Trait Anxiety Inventory,STAI-T)和情绪调节问卷(Emotion Regulation Questionnaire,ERQ)对其焦虑水平以及认知重评和表达抑制2种策略的使用习惯进行调查。按照STAI-T得分将其分为高特质焦虑(high trait anxiety,HTA)和低特质焦虑(low trait anxiety,LTA)2组,其中HTA组28例,LTA组29例,并采用内隐和外显情绪调节任务分析比较2种策略对负性情绪愉悦度和唤醒度的改善效果,以及外显条件下2种策略的难度和成功度差异。结果①2组均习惯于使用认知重评,而较少使用表达抑制[t(27)=3.94,P<0.001;t(28)=11.33,P<0.001];相较于LTA个体,HTA个体表达抑制的使用频率更高[t(55)=3.02,P<0.01],而认知重评的使用频率较低[t(55)=-2.20,P=0.02];②内隐条件下,相对于中性启动,认知重评(愉悦度:2.56±0.11 vs 2.73±0.12,P<0.01;唤醒度:6.68±0.18 vs 6.51±0.20,P<0.05)和表达抑制启动(愉悦度:2.56±0.11 vs 2.86±0.11,P<0.001;唤醒度:6.68±0.18 vs 6.30±0.20,P<0.001)都可改善2组被试的负性情绪体验,且表达抑制的效果更好(愉悦度:P<0.001,唤醒度:P<0.001)。③外显条件下,认知重评(愉悦度:2.92±0.12 vs 5.09±0.09,P<0.001;唤醒度:6.43±0.20 vs 4.33±0.21,P<0.001)和表达抑制(愉悦度:2.92±0.12 vs 4.34±0.09,P<0.001;唤醒度:6.43±0.20 vs 4.22±0.22,P<0.001)均可显著改善HTA和LTA个体的负性情绪体验,且认知重评对愉悦度的提升优于表达抑制(P<0.001);不同特质焦虑水平间比较显示HTA个体对两种情绪调节策略的使用均显得更为困难[认知重评:t(55)=2.16,P=0.02;表达抑制:t(55)=2.92,P<0.01],且表达抑制的情绪调节成功度更低[t(55)=-1.88,P=0.03];对HTA个体自身而言,使用表达抑制的难度要大于认知重评[4.00±1.81 vs 5.00±1.80,t(27)=-2.78,P<0.01],且成功度更低[7.04±1.00 vs 6.64±1.13,t(27)=2.09,P=0.02]。④比较内隐和外显条件下的情绪调节效应,发现高、低特质焦虑个体外显情绪调节对愉悦度(外显重评vs内隐重评:5.09±0.09 vs 2.73±0.12,P<0.001;外显抑制vs内隐抑制:4.34±0.09 vs 2.86±0.11,P<0.001)和唤醒度(外显重评vs内隐重评:4.33±0.21 vs 6.51±0.20,P<0.001;外显抑制vs内隐抑制:4.22±0.22 vs 6.30±0.20,P<0.001)的改善效果均优于内隐条件。结论高特质焦虑个体存在认知重评使用相对不足、表达抑制使用偏多的特点;在内隐和外显条件下,认知重评和表达抑制均能有效改善高特质焦虑个体的负性情绪体验,且外显情绪调节的效果均优于内隐。
文摘尽管从方法运用角度对文史文本深度翻译的探讨已经相当丰富,但在实施深度翻译方法之前,确立指导原则的重要性仍然不容忽视。这些原则为文史文本深度翻译实践提供了指导和规范,确保了深度翻译的准确性和一致性,并具有更广泛的适用性。在翻译威尔森的英国通俗史畅销书《后维多利亚时代人》(After the Victorians)中,笔者较多地运用了阿皮亚最早提出的深度翻译方法,采用的具体分类是曹明伦提出的显性深度翻译和隐性深度翻译。本文将对曹明伦重新归纳出的显性深度翻译与隐性深度翻译的方法做一简要介绍,包括隐性深度翻译的提出过程,然后重点结合笔者翻译《后维多利亚时代人》的实践,讨论一般史学著作深度翻译应遵循的原则。在讨论中,本文将涵盖上述两种深度翻译方法的操作与例析。
文摘It is known that the Allen-Chan equations satisfy the maximum principle. Is this true for numerical schemes？ To the best of our knowledge, the state-of-art stability framework is the nonlinear energy stability which has been studied extensively for the phase field type equations. In this work, we will show that a stronger stability under the infinity norm can be established for the implicit-explicit discretization in time and central finite difference in space. In other words, this commonly used numerical method for the Allen-Cahn equation preserves the maximum principle.
